I ran Castles and Crusades years ago which stripped out attacks of opportunity - but I never did anything with miniatures (why would you when they matter so little?) just theatre of the mind or the occasional locational sketch.
This is basically the main result as far as I can see - to make the game less miniature dependent - so It would seem odd to strip them out and then to keep using miniatures.
The thing to remember is that the grid gives weird results. It's perfectly rules legal for example to disengage, move your speed through a door and then object interaction the door closed. You can also run around three people who are standing still and do something (perhaps pull a level to open a pit or something) which they would logically try to prevent you doing, while they stand perfectly frozen in place.
If you can move without any restriction then this becomes more of an issue. If it was theatre of the mind and someone breaks free and turns to run it would tend to be assumed that the PC is immediately following*. Basically if there are no rules for common sense restriction on movement then the GM (if they're any good) has to override the rules and the utility of the grid is further degraded - what exactly is it there for then?
*GM: He turns to close the door in your face.
Player: I leap forward and try to shoulder charge the door preventing it being closed.
GM: ok make a roll.