I have no way of knowing about water drainage but that should be established before doing anything. I'm not a fan of asphalt sidewalks but I'd have no reservations about laying asphalt over concrete, it would actually hold up better than if concrete is removed. I'd pressure wash the walk fill cracks with urethane caulk . I've had public parking lots repaired that were in worse shape than what I can see in pictures. If you want new asphalt I'd lay over existing if it didn't cause drainage issues.

Thanks. i think the pictures dont convey very well but the grading where the concrete meets the asphault is very poor which I think is the main reason they want to rip out existing asphault stone over the top of everything and regrade away from the house.

I feared as much but as you say it's difficult to tell from pictures. That brings us back to square #1 where so-called pros don't agree.

Getting the drainage to move water away from the house foundation is probably the most important issue within your question, I would let that be your guide as to whether the concrete stays or goes. Don't take somebodies quick answer that 'things will be ok', get a level, sit down on the concrete and scope things out for yourself. Can asphalt be laid over concrete? For sure! Concrete highways are routinely resurfaced with an asphalt topping.

The walkway needs to be removed. There isn't enough space to add a layer of asphalt over the concrete. See where the door threshold sits just a smidge above the concrete? And the glass block windows?

ETA: The concrete walkway is a bit of a barrier to cut down on tracking black stuff into the house when the asphalt is freshly laid.