From your description you seem to be talking more about "the experience" than how vinyl actually sounds.
Actually, in most cases, the situation with the output power on tube amps is reversed from what you described.
Most solid state amps are what we call "load invariant" - which means that they deliver the same output voltage regardless of the load (within reason).
With amplifiers that follow this "rule", you will get more power into a 4 Ohm load than into an 8 Ohm load, with the same volume setting.
Because of this, most solid state amps are rated to deliver more power into low impedance loads.
In contrast, most tube amplifiers use output transformers to match the load impedance seen by their output devices to the impedance of the load.
(Power tubes work best into very high impedances, on the order of a few
thousand Ohms; the output transformer matches this to the 4 - 8 Ohm load presented by most modern speakers.)
However, most output transformers have separate output taps for specific speaker impedances, and most have at least a 4 Ohm tap and an 8 Ohm tap....
And, for MOST amplifiers that have multiple taps on their output transformer, their power output rating will be identical into each of those impedances.
(So, for example, a typical solid state amp may deliver 50 watts into 8 Ohms and 100 watts into 4 Ohms, while a typical tube amplifier will deliver the same 50 watts into either.)
Note that this applies to virtually all amplifiers designed to run speakers - but many headphone amplifiers exclude the expensive transformers.
(Headphones require relatively little power so getting a lot of power, or good efficieny, really doesn't matter with a typical headphone amp.)
"Clipping" refers to a very specific type of distortion commonly caused by overloading an amplifier.
The waveforms are actually "clipped off" and become flat on the top and bottom - because the amplifier cannot keep up with what it's being asked to do.
Clipping results in a rather distinctive - and unpleasant - sort of distorted sound.
You are certainly more likely to cause an amplifier to clip if the amplifier is under-powered and the speakers are inefficient - but you can avoid doing so by turning down the volume.
(In general, most amplifiers can actually "run" most speakers, as long as you don't ask them to deliver more power than they are capable of putting out...)
Well, given everything that goes along with Vinyl, I do find that it "sounds better".
May not be technically better, but there's much more involved with listening.
You put the LP on the player, carefully brush it, select the right speed and gently set the needle down, then raise the volume on the amp.
Listening to Vinyl is so much more intimate and therefore "feels" better.
I don't need an expensive player, cables, or amp, but they look great and that helps the "sound experience" immensely!
What I've been wondering, but cannot find the source anymore:
Some tube amps deliver significantly less power at higher impedance levels and vice versa.
If you use a 5W tube amp on a Focal Grande Utopia (impedance ranges from 2 to 16 ohms), you're bound to hear differences to a more powerful amp, because the SPL at different frequencies will be audibly different. (we're talking 3dB+ dips and rises in the curve)
Would this already be considered "clipping", because no sane person uses a 5W amp for such a hungry speaker?