Standardising free invokes as spendable for compels will break the fate point economy and pull the teeth out of compels.
The fate point economy is one of the only things that the Core book and Toolkit tell us not to mess with much, because it's the heart of the system and balanced very carefully.
A free invoke is a +2 on a roll. It can only be spent on one very specific aspect, so it's limited in the kinds of rolls it can benefit. It doesn't guarantee that a thing will happen in your favour; it just increases the likelihood. Most of the time, a fate point spent on an invoke vanishes (unless it's invoking an aspect directly attached to a character for whom the invoke is detrimental).
A compel says that a thing is true. It always establishes a dramatic fact and always gives a character a fate point immediately to help them deal with that new drama. The fate point it grants is free to be used on any aspect, or to declare a story detail or decline a future compel or power a strong stunt.
This is a major difference. If compels can be forced without any benefit to the person being compelled, using a currency that can be spontaneously generated by a single action, then compels will get over-used and lose their dramatic power. Similarly if compels can be bought off with free invokes, it stops being a hard choice to do so. The purpose of a compel is to drive the story forward and make it interesting, and players are encouraged to buy into this because they get fate points from it. Making compels easier and less rewarding dilutes the crisis/victory cycle on which the game thrives.
And perhaps most importantly: while invokes usually remove fate points from play, compels usually add them to play. Applying free invokes to compels will drastically reduce the number of fate points in your game.