Alot of classes need to be fine tuned, depending on the game. All too often we have Generals with enough speed to make them titans, but our swordmasters are fail because they only need half the speed they get to dodge the enemies and can't do any damage, and while Warriors indeed do have epic HP and Str.... Generals do it, with defense to boot, and knights are much easier to level up than axe fighters. And Archers haven't been useful since like... FE4.
Then come the mounted units, whose superior movement hampers their caps. What kind of crummy balence is that? mountees shouldn't even have similar stats to infantry because they're on a spoony horse.
And then you get character-exclusive problems. Heros on the GBA aren't bad themselves... but Raven in FE7 is a horrible merc. Low con, low defense, he's a swordmaster in hero's clothing. Same with Guy, who's stupidly high 70 speed growth is better suited for a thief, leaving Karel as the only worthwhile swordsman (not counting Lyn).
Then you got weapon using balences. Most units can use swords, some lances, almost none axes. In general, theres...
Swords: Mercs, Myrmidons, Lords, Cavaliers.
Lances: Cavaliers, Knights, Pikemen (which you dont get much of ever)
Axes: Fighters. Sometimes a pirate OR a brigand.
Bows: Archers. Lulz.
And now, lets compare what each class is "supposedly" good at:
Mercs: A high powered balence between strength, skill, speed and HP, sometimes defense.
Myrmidons: high speed and skill with average to low strength and defense
Lords: lulz Overpowered (but theyre lords so its ok).
Cavaliers: High skill combined with good attack and defense and passable speed.
Knights: Epic Defense and HP, good attack and respectable skill. Crap speed.
Pikes: pre FE9 they were AIDS incarnated. Now they're just mercs with spears. I think.
Fighters: HP and strength. SUPPOSEDLY decent speed and defense with asinine skill, but hardly ever seen.
Brigands: Fighters with even more HP and less skill.
Pirates: Fighters with a speed stat worth noting.
Archers: Downgraded mercs with bows.
Even when going off their original "intents", there's still balancing problems. Mercs should be average all around, myrmidons should likely have at LEAST average attack (masters of killing blows and all). Cavaliers as enemies should be slower than mercs but compensate with better attack, skill, or defense. As characters they need to be varied depending on the character, ie the Kains are high attack and speed, the Abels are high skill and defense, or something. Knights are good as is, its GENERALS that are broken. Pikes should be slower, more durable mercs, something of a middle ground between mercs and knights. Fighters are good in theory, they just need better characters that live up to the claims. If brigands join the party, their ability to cross mountains needs to have more use. Same for pirates and water. Archers should be just like mercs, but with bows, perhaps.
And while FE stretches the realism pretty far, a little bit of real life basis wouldn't hurt the series. Mercs come off as men-at-arms, which were lightly armored skirmishers with swords. So they should have good HP, speed and skill, with str and defense not far behind. IE: If they have 9 STR, they'd have 11 Skill, 11 SPD, and 9 Def. Myrmidons are speedy killers, and therefore are lacking in defense and endurance but good in dodging and killing, IE: 9 STR, 11 Skill, 15 SPD, 5 DEF. Cavaliers are mounted knights, which were elites with high speed and defense to chase down infantry, IE: 10 STR, 10 Skill, 10 SPD, 10 DEF. Knights as stated are ok as is mostly, IE: 12 STR, 8 Skill, 5 SPD, 15 DEF. Pikes historically were heavy infantry meant to counter cavalry and such, and would do good to be based off the merc, IE: 11 STR, 10 Skill, 9 SPD, 11 DEF. Fighters are assumedly skirmishers, but with higher attack and lesser skill, IE: 15 STR, 6 Skill, 9 SPD, 10 DEF. And finally come archers, which historically were lightly armored, similar to skirmishers, but armed with bows, IE: 8 STR, 13 Skill, 10 SPD, 9 DEF.
... and wow, this came out much longer than expected and sorta rant-ish, but I hope someone enjoys the read

You seem to have quite a good grasp of things. I have to ask, though, what level are those stats mentioned for? I'm not used to seeing non-20/0 and 20/20 level stats in plurality.