Csontos, I play in a band and have played sting bass in orchestras since I was in 7th grade. Not that that makes me an expert, but I do attend a lot of concerts. I agree that concerts with amplification are anything but warm.
But if I go to an unamplified concert, I like to close my eyes and imagine listening to a stereo. Try it sometime- and critique what you hear- is it too bright, too warm? What I find is that warmth is more often the thing I hear rather than bright and harsh, the latter being a common hallmark of solid state, hence the existence of this thread :)
Tubes BTW do not have an emphasis on a certain range of frequencies. A lot depends on the amp!! What is commonly associated with the 'tube sound' is the 2nd harmonic, which does not have to exist in a tube amp as the harmonic distortion signature is highly dependent on the topology of the amplifier circuit. This is true whether tube or solid state. If you recall, triodes are universally regarded as highly linear; moreso than most semiconductors, so where does that 2nd harmonic come from? It comes from the topology.
For example if you design to be fully differential and balanced, the primary harmonic product will be the 3rd harmonic, not the 2nd.
Transistors have a non-linear capacitive aspect that is multiplied by the current through the device at their junctions. This property is well-known, for example there is a device that is used for tuning FM radios known as a varactor diode that takes advantage of this capacitance.
This aspect makes it difficult to avoid odd ordered harmonic distortion and despite large amounts of negative feedback, will remain present in solid state amps where it is absent in a tube amp. Because our ears use those harmonics as loudness cues, they are more sensitive to them than state of the art test equipment- we can hear their presence quite easily while they are hard to measure with test gear.
So as I see it, the point of this thread is what amps are lacking this particular distortion while also being solid state? The answer is 'none' and is part of the reason the tubes/transistor debate has raged in the audiophile world longer than the existence of the Internet.
Audio is often a set of compromises, in engineering parlance certain aspects are sometimes deemed 'negligible' when actually they are not. Trace amounts of odd ordered harmonic distortions are an example.
So again- to Pontifex, consider a tube amp- they are not as unreliable as you suggest in your initial post. You are going to be chasing the Holy Grail for a long time in the solid state world if you do not. So if you really can't do a tube amp, just accept that such will be the case and Good Luck!