I strongly feel that removing racial ASI would simply reduce the number of race that players will play. Why play anything else than human if all ASI are floating or related to background or culture? Of all the power races give, the bonus feat at first level is the strongest. The trade off is the loss of a +2 for a +1, Darkvision and one or two other knicknacks that can be useful but not life saving. If even humans get their +2/+1 floating in the air ready to be spent as they wish, why do something else than a human?
Racial ASI allow the following
Strong character concepts from a min/max view:
Choosing fighter for a dwarf is always better than for a tiefling or gnome. The bonuses are there to encourage dwarves to make cleric, fighter, paladin? Not that the dwarf can't be a good thief or wizard. It simply means that more effort will be required of the character to perform on the level that an other race, favored by the system, will be able to.
Allows the building of underdog character concept without gimping the character forever:
The example of the dwarf can also be taken. A dwarven thief will have a harder time than a halfing one but it can lead to a strong melee type rogue with a good, very good armor class or a lot of HP in the case of a hill dwarf. A high wisdom and resistance to poison helps rogues a lot. Just as a dragonborn thief, even if out of the norm, can perfom as good as a halfing when level 12 is reached. It leads to surprising character builds that, if the DM is honnest enough, will surprise even the NPC. What? That half orcs thrown a fireball at the guards? (incredulous look from the guard's captain).
It fits with players expectation of fantasy genre, especially new ones.
New players (young ones and even older ones) have expectations. They want their dwarves to be grumpy and rough. They want their halfing to be merry fellows with hearts of golds (and their pockets filled with gold too!). Is it that bad to allow the expectations to be the norm? New players might get repulsed when they see their first dwarven bard, but if the dwarven bard keeps being rare they will accept it better. Not that some players will never accept, just that shaking ones expectation is not for every players. Old players might find it tiresome that they can't rely on stereotype when assessing an NPC. Players like that their expectations are respected. They like to be shaken up once in a while, but when the underdog is no longer an underdog and becomes the norm, the sense of wonder quickly goes down the drain and a sentiment of Blasé appears.
Ho.. another dwarven bard/warlock or whatever... (yawn) When the unexpected is well, unexpected, a sense of wonder is brought up and a lot of questions appear in their mind wheter they want it or not.
I know that some old players and DM would like floating bonuses to explore more character concept without being gimped at the start. This is entirely normal. What I would recommend is to do it in their games for a while and tell us if the variety of races really got better or if it has been reduced in favor of fewer races. I expect that the humans, and half elves will become prominent (and maybe dwarves too. Floating bonuses and armor proficiency? Count me in. All my wizards would be mountain dwarves. +2 to con, +2 to intel, resistance to poins and armor proficiency, the deal of the century! Even hill dwarves would be great with the additional hp every level).