I've always thought of those little props like the Bowzone or the bowbuddy as 'reference points' - sort of like using a map when you are in the car or maybe using a compass. How are you supposed to know where you are (kinesthetically speaking) if you don't have some way of making an estimate?
On the other hand - I would worry about those specific toys because (when your child is using them) the body will try (consciously or not) to adjust to those toys which can create unnatural tensions - especially with the bowzone. Furthermore, a child can become unnecessarily reliant on those little 'reference points' thereby falling into sloppy habits.
(Incidentally, a well known RNCM violin teacher uses a metal type gadget similar to the bowzone .. but again - it can mess up the shoulder/collarbone/shoulder blade alignment)
If one of my students really liked one of those toys, I would say fine - but you use it for 3 minutes (or whatever) of your practising and then do the equivalent time without. Novelty can be a wonderful thing when it comes to practising.
as for THOSE specific gadgets, it might even be better to do the matches stuck into blue tack - either side of the strings to create a 'pathway' (an errant bow will knock one or both matches over) .. and for bowbuddy, a corn plaster strategically placed on the heel of the bow (for the thumb) along with more blue tack on the stick (as a reference for the index finger & one for the pinky too - or another corn plaster) Much less expensive, much more transient and while not as 'gadget-y' does essentially the same sort of trick - in providing reference points.
Lastly, I'm not sure that it's helpful for teachers to make ultimatums. Discussions (during the paid for lesson time) might be more helpful and maybe more respectful of the child too ...... everybody (parent and teacher included) can learn something new....