Shoe laces are more functional.

Highly debatable.

For starters, shoe laces need to be tied, and they come undone. To use Velcro straps you simply have to press them firmly into place, and they take quite a lot of force to undo improperly.

The fact of the matter is the primary reason most people, by a huge margin, chose laces over Velcro is aesthetics (which Velcro sorely lacks).

Trust me--shoelaces provide a substantially better fit, support, and closure, despite being somewhat harder to use. Shoelaces are also replaceable in case of wear. Also, shoelaces are a standard and one might not be able to find the right shoe with a Velcro closure.

If all shoes were built with those things in mind (like say, boots are), then I might buy that. However in most shoes none of those things seem to be given strong consideration.

Well, don't buy impractical shoes then, no matter how nice they might look! (A-ha, we're back to the same argument then.)