> would a single ended tube amp make a good headphone amp?
Fix what's broke: it should be fine about the way it is.
5 Watts into 4Ω is 4.5V RMS. 4.5V RMS onto 32Ω is 0.6W; on 300Ω is 70mW, perfectly acceptable headphone power. Running lightly loaded like that the THD will be low and mostly even-order.
Just to keep the OPTs from arcing, I'd put about 10Ω 10W on the secondary permanently. And to reduce accidents with 0.6W into 32Ω I might put 22Ω between the secondary and the headphone jack.
It already has volume, balance, bass, treble controls. Funky old passive tone controls, I'm sure, but they were always pleasant. The 12AX7 is plenty to recover the loss in the tone controls and bring it up to 6BQ5 grid level.
I really would not change a thing, except all those caps look old and decrepit to me and I'd probably replace them all without much testing. Even if they measured good now, a few hours of voltage might be the last straw. I'd double the uFd of the audio caps (replace 0.01uFd with 0.02uFd), and at least quadruple the power supply caps (100uFd in place of 20uFd). Headphones might need even more smoothing: consoles like this only reduced hum enough so you would not hear it a few feet away; with headphones you have to go much cleaner. It might even suggest adding another R-C section to the power chain (L-C if you have the iron or cash).
The other way to go is lose the tone controls and apply negative feedback. For a speaker amp, I'd be real tempted. For a headphone amp, the only strong reason to add NFB is to extend the bandwidth of the output transformer, which may be no better than the 8-inch speakers it originally drove.
Did you actually pay $50 for this hunk of junk? {sigh} I can't remember how many of those I've thrown away over the decades. It probably cost less than that new; or rather, $100 bought this amp, a couple 8" speakers with 3" tweeters, a turntable, and a "Mediterranean Walnut Furniture-Grade" cabinet. My father still has one, Big-Name-Brand (RCA), up in the garage. If the birds and bats have not nested in it, maybe he should eBay it.