The first two walls above are very 'old school' Bali. A lot of people, even locals, have moved past this amount of over the top and expensive ornamentation. The fourth wall is a plain concrete retaining wall with expensive looking stone cladding. The third, the river rock retaining wall, is probably the best in terms of price vs. aesthetic balance and is definitely a step up from batako, though it still uses a lot of concrete mortar. And by the way, the plain batako walls are all over Bali, not just in the South.
To the OP, the gabion basket method, while quite popular in places like Australia and Singapore, has for whatever reason not really caught on in Bali (as you have discovered) so your average contractor won't know much about it. Interesting concept though, as it doesn't use cement so it's arguably more sustainable. It probably does need some sort of solid base if it really is a retaining wall. This link has some interesting observations on retaining walls:
https://www.mrfixitbali.com/walls/retaining-walls-151.html. Nothing wrong with gabion baskets in my book if you can find the quality and size of the baskets you need, as well as a competent contractor to do the work. Good luck.
