You should do whatever adds to your setting. If that means there's no 1h, d8 finesse weapon? Well, so what.
What I have realized however is I don't have a rapier. And by rapier I don't mean "long thin stabbing sword". I mean "one handed finesse-able weapon that does 1d8 dmg". As a result, a character wanting to fight with a one-handed weapon would be limited to 1d6 dmg weapons.
Now my first instinct here is "this isn't a problem, high dex characters have it too good with dex being so useful all around anyway". But... well I haven't played the game yet, and most (I hope haha) of you have. Would "forcing" dex-based characters to use smaller weapons be a big issue? Or is it a small nerf that might well be needed (seeing how good dex is).
Maybe, but I'm not sure I'd consider those swords finessable.
The rapier was likely used because it was very much a backup weapon after you were no longer able to use your musket/bayonet or pike and they likely owned one for civilian use.
The reason that the cavalry were issued broadswords instead is that it was their primary weapon: they were expected to fight in melee using it.
Re Pata: based on my fairly brief research, the blade is rather hefty, although a small majority had rapier blades on them (maybe 5%). I'm not really sure how to stat it to be honest - it's like a longsword, but how to account for the gauntlet part and how it impedes handling?
Sure, but consider this: in D&D you have on the one hand the shortsword, a light finesse weapon, analogous to the Roman gladius and other ancient swords, and on the other hand you have the versatile longsword. There's a gap between the two that represents the majority of sword evolution in the medieval period: the spatha and its descendants, the migration period, knightly, and arming swords. They were neither light (because you couldn't readily wield two of them) nor versatile (because they weren't made to be wielded with two hands).

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.