I actually paid for a domestic non-ps flat bed redeye flight, SFO to EWR just before p.s. service switched to EWR. No pillow, a blanket you wouldn't lend a dog. I was scathing in my feedback, as my reaction was United is way too stupid to be entrusted with such equipment, and I already knew this. I was way too stupid in trusting that United had reformed.
The classy move would be to buy enough pillows for the cabin (they can't be expensive) and hand them out if you can get them aboard. One would probably be stopped at boarding, in which case one could begin cursing over United's incompetence, explaining that there may be paying passengers in first who expected better. Then stand aside and hand them out to each first passenger as they scan their boarding passes.