Let's start with the positive: When Rose joins the party halfway into disc 1, the group is made up of Dart, Lavitz and Shana. Dart, as the main character who always has to be part of the active party, is a balanced fighter who mostly sticks to physical attacks. Lavitz' speed is on the slower side, but he hits hard. Shana has low physical stats in offense and defense; her strength lies in magic attacks, which are executed with items that you continuously find in chests or with Dragoon spells, though at that point, only Dart has his Dragoon Spirit. So when Rose joins the party, she's a valuable well-rounded and versatile companion who rivals Dart in being the balance of the party, seeing how her speed is higher, her initial Dragoon spell is capable of healing and her magic stat is higher than Dart and Lavitz'.
I've seen many people kick out Shana at this point for various reasons: 1) Bow users like Shana receive no Additions in the game, which means there's no fun in working towards maxing out Additions, and there's no excitement when obtaining a new Addition. 2) Shana does not have her Dragoon Spirit yet. When she receives it later on (also on disc 1), her initial spell is a powerful single-target healing spell, while Rose's deals damage and heals the entire group. Healing at this point also isn't as vital yet and can easily be handled with items. 3) Shana's physical attacks deal low damage, especially when your other party members are Dart and Lavitz. Switching out Lavitz to have both Rose and Shana in the party drastically lowers damage output. The player may also not have as many magic items yet, or be hesitant to use them since they've only just started out.
Rose already being in possession of a Dragoon Spirit when she joins is also an asset because it means she can start accumulating SP to level up her Dragoon Level right away, not to mention Astral Drain dealing a lot of damage in boss fights. Rose's Additions are easy to hit for those who have trouble with the battle system's timed triggers, whereas Lavitz' later Additions take some getting used to. She also has fewer Additions than other members, which means she can unlock her final Addition with less successfully executed Additions.
When Haschel joins late into disc 1, Rose is still a strong character – the same goes for when Meru joins on disc 2. Haschel has quite good physical stats and has high speed, whereas Meru has low physical stats, but high magic stats and the highest speed in the game. And here's the negative: By that point, it's clear that Rose is the party member with a definitely hybrid role in the group, and although she is balanced, she also doesn't excel in anything. Unlike Dart, she isn't a mandatory inclusion either. Another way to phrase this is that she becomes pitifully average and her usefulness wears off starting from disc 2, especially once the remaining party members receive their Dragoon Spirits (Haschel at the end of disc 1, Meru at the end of disc 2) and can start leveling up their Dragoon Level and cast magic. Once you're that far into the game, you're not just looking to have a group that can quickly dispatch random monsters – you want a group that's balanced, which typically means a hard-hitting fighter (male characters in the game) next to Dart and a magic caster who can heal (female characters in the game).
Rose doesn't become dead average starting from the midgame just due to her lack of specialization though. Her HP is the second lowest in the game, and her physical defense is average, while enemies hit harder and harder. Her Dragoon spells are useless later on (in contrast to Astral Drain's usefulness early on) because Astral Drain no longer heals enough, and her second and third spell (which inflict Fear and Instant Death respectively) are spells meant to target random monsters (Instant Death naturally does not work on bosses), whereas players typically save their SP to transform into Dragoons during boss fights. Due to her spells being designed as a combination of damage and secondary effect, none of them specialize in damage either, making Rose lag behind when everyone else eventually obtains more powerful single- and multi-target spells.
By the third or fourth disc, Rose thus brings no utility to the party at all (even a powerhouse like Albert can cast a group damage resistance spell!), and her Dragoon form is useless in its entirety once even regular Additions deal far more damage than D-Additions. Sticking Rose with a healer late into the game means having a party with low HP, low physical defense and rather low physical damage, whereas sticking Rose with a physical attacker means relying solely on items for healing. This still works most of the time, but it is suboptimal and may make certain boss fights harder. The other female party members are just better choices due to their healing and status recovery spells as well as their high magic stat. While Rose may still be a consistent attacker of average speed by the end of the game, what made her balanced and great in the early-game is also what makes her average and unappealing in contrast to other choices (except for Kongol, who's considered the worst party member by many) by the end.
You can most likely beat the game with any party and there are many great party combinations out there (which, in my opinion, do not include Rose in later parts – it'd be a different matter if Dart could be switched out), and really, playing a JRPG is all about running around with an active party consisting of characters you like – as characters and/or as party members. If you'd like to use Rose, I recommend one of the following approaches:
A) Be flexible. Use Rose in the early-game, but don't hesitate to switch her out once her stats and utility fall off. If you don't, you'll neglect training Additions of other members, which may be much more useful to you later on, and the sooner they get their final Addition (as well as their Dragoon spells in some cases), the better. Strongly consider training Haschel as a fast damage dealer as well as Shana or Meru as healers and mages, especially by the time you receive their Dragoon Spirits; they'll all serve you well later on.
B) Switch between parties for field sections and parties for boss fights depending on your needs. It may not be optimal if you want to get the most out of experience distribution and want to raise Dragoon Levels or work on your Additions, but I prefer having Rose in random encounters compared to boss fights, whereas it's the opposite with the other female characters (unless you always carry around a lot of magic items that target all enemies).
C) If you keep Rose for boss fights, switch between a hard hitter and a healer/mage for the third party slot depending on the boss fight. Consider using Albert for his damage mitigation spell as well. As for the final boss fights, running both Rose as well as a healer is possible; I'd suggest dividing HP boosting equipment (see below) between the two in that case.
As far as late-game equipment is concerned, I recommend the following: Consider giving Rose the Dragon Helm when you obtain it halfway into disc 3 for the extra defense and the 50% HP boost, since her HP is extremely low. Don't miss the Gladius in a corner of the Death Frontier at the beginning of disc 4; it's her best weapon until the final boss fight and has a chance to trigger instant death in random encounters. Give her Dancer's Shoes for boosted speed, since she's the slowest of the female characters. For accessories, I usually equip her with Therapy Ring, which helps her replenish some HP each turn. If you don't have enough Therapy Rings for the characters you'd like it on, Physical Ring with its 50% HP boost is a good substitute; higher max HP also means more HP replenished when defending. Mage Ring with its MP recovery per turn is an alternative if you'd like to spam her instant death spell in random encounters, but magic attack items are generally the better, faster and more reliable choice if you have the inventory space.
I'm not going to bring up the few pieces of ultimate armour here because the average player won't be grinding for that much money in a game that does not require one to grind. Rose's "ultimate weapon" is also only received right before the final boss (when you can no longer return to the optional bosses), so it doesn't affect her itemization.