The problem with TPU is that pushing flexible filament through a PTFE tube (and retracting it) causes friction and binding. Any external (automatic) feeding source is going to suffer from this same problem. Its not the multiple spools in the AMS that cause the issue (although going through yet another PTFE path doesn’t help) its the physics of feeding that filament all the way to the extruder (and pushing it in with enough force to part the gears). The longer the run, the more difficult this is and each time you have a filament change its yet another chance for failure.
The TL;DR is that your success or failure with TPU will not change with an AMS that has fewer rolls.