Every professional has their own preferred system or method of doing something. A high quality outcome is of importance rather than the various methods that can be used. Not sure why the walls would buckle when emptied? Maybe the professional who mentioned this has had them move before and crack the shell. Have a chat to a few companies and ask them why their process is better than the others.

We are almost done - some metal artwork and filter box to go before planting. Thought you all might like to see what we ended up doing…. Pool & tiles by pool company, everything else done by ourselves. We are extremely happy with the waterline tile colour - they show up differently all times of the day which is a lovely surprise. Ezarri Glass Mozaic waterline: Space Capricorn Capping Travertine

For my mind the raised one not only looks better but also, for some reason, feels nicer when soaking (maybe it's a "Lord/Lady of the Manor" thing :) ).

A pool of any sort is going to be expensive. The photos imply quite a steep slope. You either need to cut in or raise up, both of which will require elaborate and costly engineer designed retaining walls. Why bother? It's a great looking natural site that could be really enhanced with a good garden that would retain the slope and be far cheaper.