Hmmm, well it seems that you don't understand much about the stats of soldiers in this game.
Axe fighters should receive + 1 defense, because of their shield.
Actually they do, but only against ranged attacks. This also counts for other shielded units, such as knights or sword-fighters.
Sword fighters should have 3 armor instead of 2, (the halberdiers and marksmen all have 2 defense, and swordsmen are carrying a shield too)
In the original game, I agree that this makes no sense. The only difference was that swordfighters were stronger. The shield basically did nothing. Anyway, swordfighters in the Remake are much more powerful than pikemen because of their increased attack and their shield bonus (which I just mentioned)
Soldiers on horseback should receive +1 defense or + 1 attack. (cavalry is meant to tear apart infantry raging across their lines, but as the game engine works it completely negates the mobility of the cavalry and always a pitched battle ensues)
Maybe mounted units are immobile in your hands or other players who are not skilled in micromanaging their soldiers, but skilled players can use mounted units to crush a routed army, or flank unguarded bowmen. An army with just a handful of knights (as little as 3) is much more powerful than one without them. But back to your suggestion: mounted units already have the shield bonus (with the exception of the vagabond!) and have an impressive +1hp (much better than it might sound. Basically, they take ≈25% more hits to kill them).
In summery, don't pay attention to those stats that you see in-game. They are very misleading. If anything here needs to be "rebalanced" it is the stat UI
