Well for starters, people would probably run at least 1 of each basic their deck runs heavily.
I can also see this breeding a new form of combo. Current combo decks run something like 10 five color lands. It'd probably be possible to trim the mana base down to just 5 basics and go nuts from there, never having the risk of hitting a mana clump. Alternately they could keep the same number of lands they run now and go crazy with Fastbond.
Making a solid mana base is one of the hardest things to do. Though it's not quite as hard as it used to be thanks to fetchlands, taking out an entire part of deck design just doesn't seem like a great idea to me.
Many decks already run at least one basic land to fetch under a Blood Moon or when staring down a Wasteland.
I’m not convinced a combo player would skip a land drop just to cut a few lands from his deck. Going crazy with Fastbond is no easier under this rule because it only allows one pitch and search per turn. So while they could pitch, search, and play the land with Fastbond, that’s where it would end.
I agree with you on the mana base issue, but even the best designed decks can face mana-screw. Color-screw is a different issue altogether, and I think that’s what you are talking about. Is removing a card from the game and missing a land drop enough of a penalty to allow a player to get the color they need next turn?