I know for a fact that car speakers are designed to be sold. So, since you bought them, you have experienced the full depth of the 'design process' of an aftermarket car speaker... from what I've experienced...

Honestly, some speakers are clearly not designed to be free air. One such example is Polk's $200 mid-line series with 6.5" drivers and separate tweeters. In a display case they sound OK because the volume of the cube they're in is small and good for them. In a car door, though, they dissapear sonically.
One of the few sort of reasonably priced speakers that don't do this is Boston Acoustics. I guess they thought about it a little more... I don't know.
So, if they're anything like my wife's Polks, they will benefit from both better amplification and an enclosure. Q-logic makes enclosures that are pre-fab'ed for some cars.
If you can leave the speakers securely mounted to the doors, it makes it easier to live with... less crap in your car to deal with... and if they're not very securely tied down, they become projectiles in an accident.
Lastly, one thing to consider is XTC foam baffles from Crutchfield. They help speakers sound better and they're cheap. I haven't tried them on the Polk's yet... it's not my car so, I don't really care.
Best of luck on your quest for car audio wisdom.