On a personal note, I've never liked randomly rolling for stats so I may be a little biased. I know some people will praise it up and down but I've never seen the appeal of having some members of the group being Olympic super stars and others only being qualified for the Special Olympics. YMMV.
Yes, well, that's stated as, "I don't see the appeal of the worst possible result of this, if the GM exercises no oversight on characters," so, yeah, you wouldn't see the appeal.
For me, the appeal is in designing a character with exterior restrictions. Point buy asks the question, "What stats to I want to have, and how close can I get to them?" Random rolls ask the question, "What can I do with this particular mess of stats?" I find answering the latter to often be more fun, and often leads to me creating more interesting characters than the former.
A well-designed point-buy system should guarantee that the generated character will be reasonably viable (just like a well-designed class does not allow one to shoot oneself in the foot too badly, such that characters meet a certain base effectiveness unless one either really doesn't understand the system, or chooses to hamstring themselves. And, by extension, a point buy system helps keep a party from being too out-of-whack, power-wise.
Random rolling generally can't guarantee either that a particular character will be viable, or that the party will be balanced among themselves. That guarantee must come from player and GM oversight.