There should be an option to get bech32 privatekeys from chipmixer for privacy and lower fees (some 50%+ fewer satoshi paid when bitcoin network gets congested). This should not be difficult, just need a bit of update with sufficient regression testing on the back office of chipmixing.
I don't think it's much of a problem on Chipmixer's end, but more so a problem when it comes to the adoption of bech32 that needs to be more widely deployed.
Bitcoin's lowering fees made people pretty comfortable with how the situation is, hence the majority of the clients don't see much need to add it, though I would have preferred them to be more active and give people that option anyway. The trend within crypto seems to be to only act when its needed, and not make sure you're ready to onboard more use beforehand.

I personally don't have much of a problem with Chipmixer not offering bech32 support yet. Even the legacy fees aren't usually topping $1 per transaction.
an upgrade to nested adresses would suffice too. I don't see why not. They're widely, if not everywhere, accepted.