This is super relevant to my interests. I saw both these guys live this year.
These dudes are totally very much based in the electroacoustic world, as previous mentioned. They use a lot of field recordings, live smaples and instrumentation and then combine it with soft synths, granular synthesis, MAX and a myriad of plugins.
Frost uses Ableton, but I have heard that Hecker uses Logic to compile his end results while doing a lot of work in MAX and Audiomulch.
For Ben Frost, there is a massive difference between stuff like"Aurora" and "Theory of Machines". When I saw him this year, it was mostly laptop/Trigger based while he would also occaisionally pick up a Telecaster that from what I could tell was going through a laptop and then into TWO fucking SVTs and 810s. It was the best thing I've ever seen. All he was doing with it was creating large amounts of feedback or simple drones and looping it in kind of semi random accompaniment to his laptop stuff.
Dude also utilises unholy amounts of compression and strips a shit tonne of some weird kinda low middy range, so it knocks your head off with supreme clarity.
Tim Hecker is much easier to kind of replicate or understand, at least to a point. He just puts an enourmous amount of work and refinement into it.
Field recordings, small repetative samples of acoustic instruments. He's really minimal in his actual notatable composition and instrumentation, and just layers things really amazingly.
Dude uses heads of granular synthesis inside the box, and I recall him favouring an Eventide H8000.
When I saw him live this year there wasn't a lot in the way of identifiable music, like his album stuff. It was really, really noisey and cool, while there would be a few familiar piano fragments here and there. Super cool.
Frost was my fav live show ever. Tim Hecer would be still in the top 5 though for sure.
I make similair (Admittedly WAY shittier) stuff utlising the kind of processes simialir to the one I outlined for Hecker. I use Ableton at utilise the Monolake Granulator MAX instrument extensively. That is the one true advantage of ABLETON for me, the partial yet seamless integration of MAX into your workflow. There is a website called MAXFORLIVE.COM that compiles all the available MAX effects and instruments, many of them free, and they can be implimented eactly the same as VSTs/AUs, while being quite a bit smaller, more stable that most free VSTs and in a lot of cases quite a bit more niche. For example, one of my most used MAX effects is a Stereo Limiter with an LFO on each side. Get some seriosuly wobbly shit going on. I also use one that is a real time kind of effect in that it has 2sec, 5sec and 1 second buffers which can record and playback audio onto new armed tracks in real time at a variety of speeds and backwards if you choose.
The mouse movement OP references would have to probably be the triggering of clips in Ableton's awesome session view. It's a pretty intuitive way to bring weird Ideas into a kind of free live domain.
A good reverb is essential, as I am sure you know. Valhalla Vintage is my fav currently, as well as a MAX effect called WASH.
BAckwards voyager mentions paulstretch and that thing rocks,a s well as the free delays/glitch stuff from Glitch machines.
Also, try sidechaining heavily processed field recodings to actual music, it can get some cool results.
Also, although it may be sacrilege around here, I enjoy recording guitar through my pedal board and straight into my interface for a lot of weirder textures. SOmetimes a dirt pedal will sound completely different, or even bad in a good way, or something like that and it can be rally inspiring in these situations.
In the end, Ableton isn't probably ESSENTIAL but session view and the integration of the MAX stuff makes in indespensible to me.
Hope some of that is helpfull, I'll have a think on it for a while and see if there is anything else I can think of. Good thread
EDIT: Holy shit that is a long post. Sorry I'm a fanboy mofo who's pretty into this kind fo stuff haha