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?