That's the other thing: not all ability scores are equal. Roll badly for constitution, and you get a free red shirt. Roll well for Intelligence and the careers adviser has only one option open for you, but roll well in Charisma and you have lots of options.
This is true. Because I give everyone a free 15, everyone has lots of options, though a few classes with dependence on several stats may be ruled out by several low rolls - eg if you roll low on all of STR DEX and CON then Fighter probably becomes non-viable. A heavy armour Fighter needs both STR & CON, though they can probably get by with CON 10 at a pinch.