I started in high-end headphones before I went to speakers. No, headphones are absolutely not giving you insights that can’t be gleaned from good speaker setup. If anything, it’s the opposite.
The driver technology and R&D investments put into headphones, even high end models, generally lags far behind that of high-end speakers. Headphones can be really good (particularly electrostats), but end of day I get more insights and enjoyment from my Tannoys.
Tube amp performance is highly dependent on the load they’re coupled to, but that’s a factor for both headphones and speakers. Speakers pose the bigger challenge, with lower impedances and the need for much higher power levels - necessitating large expensive PSU’s and huge output transformers (for non-OTL designs). So again - on speakers, tube amps will generally display bigger sonic differences versus each other and versus comparable SS amps. Of course there are exceptions, and some of the OTL tube headphone amps popular in the 2000s featured extremely high output impedances which had a MASSIVE effect (coloration) on the distortion profile and frequency response of most headphones. Though damn, did that ever sound good in some case ("flat" headphones often run the risk of being an incredibly boring listen).
The usual cited advantage for headphones as an evaluation tool is getting the room out of the equation - and that’s true to some extent. But the reality is that the headphone frame/chassis/cups, in combination with your head & ears, serves as a defacto "room" by which the sound is colored anyways. Also, I’ve never had any problem taking an audio component over to a friend’s speaker system (completely different room) and hearing the exact same sonic signature & net effect as I did in my own room. As long as you don’t pick an awful room (closet, greenhouse), pick a very wrongly sized speaker for a given setup, or totally botch the setup & positioning optimizations - I think the effect of room acoustics has been a bit overplayed online in the last (say) 15 years. Acoustic panel makers love to sell...panels. But for me, the components you choose and their "synergistic" combination has been easily the dominant factor in whether a system will be enjoyable or just chum for the audiogon classified waters.