We are addressing the slowness of KK 2.0. It will be right soon.
From our developer,
As we talked about pre-launch, your new site has some performance issues due to the sheer volume (100k+) of entries, which is stretching the limits of both Craft and the database itself. Every time we pull a listing page that huge number (or the 80k+ in KKH alone) makes the queries drag. It's one of the issues you had in the old EE site as well (although ancient code was a bigger one) because of that huge size.
Our hope was that caching would provide enough of a cushion to the site to make performance stable, but after pushing to production today it became clear pretty quickly that we were maxing out available resources. It's gotten a bit better as the cache has filled out and fewer uncached pages are being hit, but not good enough.
One solution, and the one we were using with the old site, is to throw more power at the problem. That gets expensive though - the host recommended moving to their Pro plan (+$50/month) or adding a dedicated database instance (+$125/month), or maybe both, to add more power to the server. I don't want to run up your monthly costs though and the web server load aside from database access is actually quite low.
We also looked into static caching, where pages are turned into flat html by the cache tool and then represent almost no load on the server, but that has 2 problems - it can't easily be used on listing page, and we can't use it on individual pages because of comments.