sure its possible... playing a (single) sample back at different midi notes, is just a matter of changing the speed you play back the sample.
however, the reason this is not commonly done these days, is over a single sample over a large frequency range often doesn't sound great... which is why multi samples over the split/velocity are used. this can also be done with Axoloti (with patching) but you need to be careful of sample size/ram usage.
there are lots of samplers still available, that can be triggered from midi.
so I can't quite see what your saying is not possible with these - perhaps you need to explain a bit more precisely what cannot be done by these, to determine if Axoloti can do it (likely) and how much patching is necessary(!)
cost (only) is not a great reason (in my experience) - as you'll soon gain an understanding of complexities the other solutions provide...* this does not mean Axoloti cannot do it (and is obviously cheaper) but it means to do the same you have to spend time implementing these things OR trimming down your requirements / expectations.
put another way, it takes 5 minutes to do a simple chromatic polyphonic sampler in Axoloti ( once you know what your doing), but implementing a Volca sample could take you 6 months.
but here is the 'rub', why would you implement a volca sample on Axoloti, when you can implement something unique, something new, something that is tailored to your requirements?
this imho, is where Axoloti shines... a volca sample is what it is, what korg want it to be, unchanging... Axoloti can mutate to what you need... where you want to take it.
(* of course, if you have lots of time, and no cash... then its a great learning experience... but many underestimate the effort, and this can lead to disappointment)