I agree with the psychology aspects, but from a game mechanics standpoint there is very little difference. Ultimately, you are adding numbers to a roll...whether those numbers are fixed or random. If the Weapon Specialization feat gave you a +3 bonus to damage rolls with a weapon, or if it gave you +1d6 damage instead, would it really make that much of a difference? In the moment, maybe. In the long run, probably not.
The random element to the system has a bigger effect than a simple modifier, or smaller, depending on the size of the random element vs. the size of the modifier. A +10 bonus will almost always be higher than a +2d6, after all.
Now, psychology reminds us that there is a chance that we could get an 11 or a 12, and some people will gravitate toward that...and psychology makes us forget that there is an equal chance of getting a 1 or a 2 (and that in all likelihood they are going to get a 7.) But man...that rush we get when we DO manage to roll a 12 is going to make us forget all about those ones and twos!
So I agree that rolling dice is more fun than static modifiers. But from a math standpoint, the difference is slight.