Well classical looping comes from tape looping and delay experiments so the usual approach for the field was overdubbing.
When Ableton live come these paradigm start shifting even Ableton wasn't conceived to that in mind but still nowadays grouplooping isn't a field itself. The nearest could be multilareying which is how common live loop artist build songs but usually at studio (and maybe very few at stage).
The thing reason behind why there are so few or zero hardware with this approach is risk vs revenue.
Looping everything and building from scratch is useful in composition at studio but just a gimmick for touring. Very few artists will grow a show from scratch and show it as "work" (to demo a work you must create it in advance) so these proposals are just experimental or ephimeral from a start point (which end in experimental exercises in the end).
If you bring pre-recorded material then it's backing tracks, more or less live but backing tracks in the end. So between bringing all pre-recorded or just few there is not so much distinguible from the crowd perspective... so why to risk?
There are some artist doing in between approach like Tash Sultana or FKJ but usually these artists are capable of perform by themselves without loops if the set wrecks. Take this in consideration too, please.
Then we have some hardware which isn't loopy oriented (in fact we have so little really focused on it) which can be used as grouplooping tools. Digitech trio+ maybe is the first grouplooping tool I know released with that idea in mind and it's more a backtrack groovebox than a looping tool if you think it twice.
The DJS1000, the Electron OctaTrack or the Akai Force are Ableton-in-a-box attempts. Even Traktor with F1 or D2 controllers could fit in that description but again the point is these weren't developed with looping artists in mind so some of them aren't even suitable (or a PITA to work with).
AFAIK the only enough flexible and suitable is the DJS1000 but pricey as Pioneer usual tier for just go looping at bars.
If we take in mind what customer segment we are trying to reach then the proper tool emerges by itself.
For bar gigs: Digitech trio+.
For Festivals (or properly budget sessions like VIP hotels): DJS1000 or Ableton Live on macbook pro.
That's an opinion of course, an educated and well argued, but just an opinion since I learn things everyday and I go wrong too often to believe I have the Gospel truth but bang for buck this is what I've learnt over years.
In fact the perfect setup for low to high tier will be a Digitech trio+ mk2 with midi clock capabilities into iPad setup with GTL for extra grouplooping backing tracks...
or
... GTL implementing some of the trio+ functions (musical note pad has some of them like build bass and drums from recorded material)
but since we live in present I just go and grab what is available.
Maybe someone develops a perfect onemanband live-arranger tool but if it never happens... probably will be due it's a market niche, not for hardware limitations or clever developers. There are both of them out there but these struggle with narrow-minded budget managers or directly with budget struggling if they are iOS developers (and in this case narrow-minded is Apple itself with its Appstore policy).
Hope it helps to set a compass in your research @[deleted] <3