I recommed Steve Reich - Music for 18 musicians :-)
Composing in the DAW is the best way to make someone else's music. Create your own creative process, then you are on the way to your own sound.
You can turn off auto-warp on audio tracks by default globally, and you can disable warp on a per clip basis as you go.
In your specific case... disable warping on your ambient track, line it up against your warped/synced "another sort of loop" in arrangement view, and then change the master tempo of the track until you find out what you want in terms of different tempos. (This is off the top of my head, and without the program in front of me. Apologies if it's vague.)
Live can definitely function as a "dumb" multitrack recorder that lets you do those things -- but, by default it has all the tempo/beat/quantize options turned on.
I saw your edited post above... I think people are reacting negatively to your criticisms because they're a bit harsh, and, I personally think it's shooting the messenger (Live). You can do the things you want to do in Live... but by default out of the box, it's not what's it designed for. Live lowers the barrier entry to making sound... the people/users cranking out 4-4 120bpm tracks likely wouldn't be making anything had there not been Live. If you don't want to call that sound art or music, that's on you. To many people, that's still music, and music they might not have created otherwise.
EDIT: Just saw your other post here (https://news.ycombinator.com/item?id=14300672) with some more specific criticisms. I feel your pain. You obviously already know how to do the thing I'm mentioning above, and are referring to more complicated scenarios. Thanks for sharing.
>What if I want the sound of rustling leaves to come and go across the course of a song?
Trigger it via MIDI as a one-shot in the sampler, for example. Sampler and Simpler params can be automated. If you want some 'arbitrary' looping, again use the loop points of Sampler and set the (re)triggering appropriately.
You can do all these things if you want to, you just have to invest enough time learning the tools.
Edit: If you respond, you may mention that you have invested the time. Perhaps you have, and I'm just misunderstanding your case or needs.