Mechanically, it costs a feat because exotics are, statwise, better than martial weapons. Asthetic/character reasons aside, if bastard sword and waraxe were martial 1 handed weapons, then who would ever voluntarily use a longsword or battleaxe? Why wield Longsword/Shortsword combi when you can have a doublesword?
One problem that occured to me with the pick up and practice method - would all classes be able to learn weapons they can't normally use? Wizard with longspears and repeating crossbows? Thieves sneak attacking with greataxes?
To make it a more attractive deal for a feat, you could group the exotic weapons by type and give several related ones for the price of a single feat.
For example:
Double weapons.
Oversized weapons (bastard sword, waraxe, etc).
Martial arts weapons.
Etc.
And/or possibly increase the number of feats. Perhaps give players free feats in exotic weaponary. e.g. every 4 levels for a fighter, 6 for ranger, whatever. Like the old style 2e proficiency system.
Another option would be that fighters/fighting type classes are proficient in all exotic weapons from the start. Although I doubt many fighters would use martial weapons after that.
Though, like everything, I reckon if it works then go for it!