I just noticed that the OP was asking about the cleaning process for re-waxing a chain, not for cleaning a new or previously wet-lubed chain. If using hard paraffin wax with minimal oil content, I believe that solvent cleaning when re-waxing may be unnecessary. There appear to be two schools of thought on this issue.
Simply putting the chain in wax should flush contaminants out of the chain
Molten Speed Wax, which has sold paraffin-based wax for some time, says that if a chain was ridden in dry or mostly dry conditions, it can simply be dipped in the wax pot without prior cleaning. The contamination inside the chain will melt off into the pot of wax. If the chain was ridden in the wet, then it's good to swish it in boiling water. This will melt off the wax on the chain, and with that any contamination that's in the wax. Zero Friction Cycling, which distributes MSW and some other lubricants in Australia, concurs with these instructions.
It's true that with this method, the pot of wax will gradually accumulate contamination, and eventually it will need to be replaced with new wax.
Cleaning the chain before waxing
The alternative is obviously to clean the chain before immersion waxing it (i.e. before putting it in a slow cooker or other device full of molten wax).
Wax treatments need to be refreshed regularly, or else they will sound noisy and wear will accelerate. I've heard 200 miles as a guide for wax service intervals, less if you want to really maximize chain life. (NB: The principle applies to drip lubes as well, it's just that the liquid likely damps the sound.) This could be a lot of work every week to clean the chain. You could mitigate this somewhat by having multiple chains in rotation, but having to clean the chain before re-waxing would still be a burden.
One plausible alternative is to combine hard waxing and drip wax lubes like Squirt, Smoove, Tru Tension Tungsten, Silca Super Secret Chain Lube, Absolute Black's Graphene lube, and probably a few others I haven't heard of. (NB: no product recommendations, I am just listing lubes I recall hearing of and that there's evidence are well-formulated.) You would immersion wax the chain, then top up with a drip lube every few hundred miles. You would then do a full clean and re-immersion waxing at a longer interval, e.g. every thousand miles. Josh Poertner of Silca is a proponent of this technique. His rationale is indeed that it keeps the pot of wax cleaner.
In terms of economics, Molten Speed Wax is significantly cheaper than Silca's wax. If you were using MSW, plain food-grade paraffin, or another good hard wax of similar cost, then you might bias yourself towards cleaning by immersion waxing. If you are using a relatively premium wax like Silca or Absolute Black's hard wax, then you may wish to consider combining with a drip lube and cleaning before waxing. Absolute Black's lube is absurdly costly, so you really want to minimize contamination in the wax pot. In a season where you're doing indoor training only, external contamination should be minimal, so contaminating the wax pot may be of minimal importance. Also, different formulations of wax use different friction modifiers, e.g. MSW uses molybdenum disulfide (MoS2) and PTFE, whereas Silca and Tru Tension use tungsten disulfide (WS2) and unknown other secondary modifiers (but Silca does not contain PTFE), and Absolute Black uses some form of graphene. WS2 is more expensive than MoS2. If you're using a WS2-based hard wax, it may be worth sticking to another WS2-based drip lube.
@Rider_X made a comment asking why not just use heated plain water in the ultrasound cleaner when cleaning a previously waxed chain. Indeed, this is the crux of the matter, and an ultrasonic cleaner isn't even required for this step. For that matter, chain waxing should not require an ultrasonic cleaner at all, nor is an ultrasonic cleaner alone sufficient to guarantee a clean chain. Nonetheless, if the OP used an ultrasonic cleaner with sufficiently heated water, I'd expect the cleaner to extract more contaminants from inside the chain than simply swishing it in water. Again, this would lengthen the service life of the wax. But again, this comes down to a trade-off of convenience for better lifespan for the wax, which is not that expensive considering that it's also extending your chain's lifespan.
As a side note, the OP's stated process neglects a step to remove the solvent. Typical degreasers, including acetone or mineral spirits, will leave a sticky film on the chain. This film will inhibit the wax's adhesion to the chain, which will increase drivetrain wear. The typical recommendation is to shake the chain in a bottle of denatured alcohol to remove the degreaser film. I would argue that if the OP must solvent clean their chain, then the alcohol bath is also required. I am not certain if the degreaser film will contaminate the wax itself.