Having seen the experiment in it's beginning (hola E and team), I wonder: out of things you didn't use, have you found the changes to be 'for better good' as well?
Yes, exactly, lots of round trips, quite expensive to calculate each. SMP, the ZKP protocol they're using, is quite expensive itself, but promises even better security and nifty set of additional features, based info from presentation linked in the article.
However, I think that ZKP is not what you want for regular authentication: just for specific cases, where ZKP properties shine the most.
Your case is a case of established trust relationship (remote party has your private key it trusts), which is somewhat different from what folks in the article suggest, hence the zero knowledge part. so, for them ZK property matters a lot, to my understanding.