Nah, the map plays well. The steps you describe often occur, but you don't have to do it this way to be succesful. To be honest, with all the push maps we have especially on Normandy maps, I personally don't want one of my favourite maps to be touched. Push mode would also influence the tank combat on this map. As this map offers the best tank combat gameplay of all Normandy maps, better leave it as it is. So imo it's one of the most exciting and versatile maps around, push would limit the flanking opportunities for tanks.
Only thing that I could imagine to work is a soft push with Allies having to cap 1 flag on their side of the river before they can attack Villers & P 123, so they don't get attacked right away. That's something that might actually work out well and Axis can concentrate their forces on the flags on the left side of the river. A tough push that needs Allies to cap all 3 falgs on their side in order to get to Villers and P123 is something I would strongly dislike though.