In the dim and distant past (in my Student youth) I have built "HiFi" amplifiers with a few transistors from designs in "Practical Wireless". These could probably be called "simple solid state amplifiers" but I doubt if they were really hi fidelity. Now, if I look inside my Sony "scala" hifi amplifier (bought a fee years ago) it looks highly complex, with ICs as well as power transistors. Presumably (?) this complexity is there for some reason??
I do not know, but the "best" (i.e. the most expensive) kit, which is meant to provide the purest sound replication (?) does not look like "simple solid state" gear to me. I am not doubting your desire, just wondering whether it is achievable in practice?
Before I moved into the realm of vacuum tubes, I had done some heavy leg work on building a Quad 606 clone. As amps go, for the power output, the quad current dumping design is relatively simple in terms of size and component quantity. The Naim NAP250 is commonly cloned and that seems to be a very simple amp with a very good rep.
I finished off doing the second one this morning.
Doesn't look too bad considering the cobbled together nature of these prototype builds. Once I've figured out how I'm going to get the proper aluminium chassis made, I can get them built properly.
I've also invested in some DC blocking PCB's and all the necessary components to build them. I've always had some residual hum on all five of my amplifiers which has made me suspicious of there being some slight DC offset.
I've made a start on building one of them. I got 3 PCB's so I can do other parts of the house.