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 is unnecessary. 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. The OP's cleaning method should, I believe, preserve the life of the wax for considerably longer. However, it is much more labor and solvent intensive.
@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.