First, I want to point out that flying characters already had this option at the cost of a single feat, Flyby Attack. Flyby Attack is different from Spring Attack in that it allows any standard action during movement, which is massively more valuable.
So this would eliminate the point of a few feats, like Flyby Attack and Spring Attack. But I have played in games where Spring Attack was explicitly changed to work like Flyby Attack (rather than being a single attack only) and had its Dodge and Mobility requirements waived, and it still didn’t get taken by anyone. I have also played characters that did take it, because it was required for something or other, and... it didn’t really matter.
In the end, positioning just isn’t that important in the d20 System (unlike, say, 4e). Ranged characters don’t have particularly stringent demands on where they stand, and melee characters typically don’t want to leave melee once they’ve closed.
So the only cases where it ends up mattering a lot are:
your melee attack kills, so you want to move on to the next thing. Ultimately, to have your one single attack be the difference isn’t that common an occurrence, and you can always just charge next turn or whatever. This can actually hurt you if you move into melee with your next target, but cannot attack – now that target gets to attack you first, without even having to move. Bad news bears.
making the difference in an otherwise-symmetrical situation (move in, attack, move out). Unless you foresee a lot of literal mirror-match one-on-one duels on featureless terrain, usually some other factor is more significant.
you have truly massive movespeed and the room to use it, and you have powerful ranged options (read: spells). By which I mean more than double that of any of your opponents. That’s pretty hard to get, and usually costs too much. But it does make a big difference for, say, dragons..
Personally, I say go for it. It offers a few more options, it seems a little more sensible, and the loss of these feats as meaningful choices is minor; they probably didn’t deserve to be feats in the first place. Just make sure to change other feats’ requirements accordingly.