Honestly I think enough basics are unlocked from the get go. It's enough to get a handle on the system and as you progress through it you get more things to pop.
There's a few things I'd like to see pop earlier, but that makes them sooo much better when you finally do get them. Teleports are a good example.
Imagine trying to learn the Anachronism missions with 40+ different types of critter in there. GYEAH. Talk about a headache. I still make mistakes in those. Oh, look... water espers don't belong... whack whack... DEFEAT... here? Crap.
Yes, if you're an RPG style completionist where you want to pop everything before New Game+ (like I can be, depending on the game) this will frustrate you. Personally, I'm taking a zen outlook on the idea... just go with it.
You can rampage the bosses pretty quickly if you choose to.