It is indeed in part a sideways move and that's why I would ideally find a class AB solid state option. However, heat wasn't the only reason to move away from tubes.
Other examples were the one-minute warm up time during which the amp is on mute, having to switch it to my preferred triode mode, having to keep it turned on in case I want to use it again in the near future, as each cycle damages the tubes and because you need to wait for a certain time before starting it up again to save tubes.
There are also security concerns with children and just the hassle of tubes: their long-term availability, searching for the ideal NOS tubes, finding the best combination, etc. Some people like tube rolling and the possibility to adapt the sound to their liking, but I would prefer an amp with no tweaking possibilities that can be just left as is. I'm being very negative here, but it's just to make the point regarding the accumulation of things that have been bothering me at different points. I do love my tubes in guitar gear (including in various pedals) and wouldn't ever imagine going solid state there, but it's just a very different use case.
The Pass lacks auto standby, which is its biggest drawback. But you can turn it on and off with the remote any time without needing to worry about hurting any component of it. And if its left on unattended, there's not the same danger as if a tube goes bad. But the current draw and heat at idle are definitely concerns on the Pass. To me, it would at least be a pretty good step in the right direction in terms of what my concerns are with my PrimaLuna, even though it's not ideal as you point out. In addition, I do believe, and hope for the price, that it would be a move up in terms of sound, as you also allude to.
You mention the Stereophile measurement look good, are there aspects I should look out for in measurements that could help me identify the amp that might work for me? I've never really tried to understand measurements.