This may very well be true - I know some manufacturers have out and out said it's a stability concern (Schiit has, for example), but it certainly could be true of other builders (what, manufacturers lying? impossible!). But it isn't like transformers don't exist. (e.g. the WA6 and the Cayin are both suitable for lower Z cans - they both cost a lot though (last I looked the Cayin had just bumped up on $900)). I know that even with some SS amps though (as I mentioned above), the manf is saying it's a no-go, but it's usually *very* low impedance (usually <16R, which is getting into speaker territory) - there's very few full-size headphones that fit into that (I can name a total of four; only one is currently in production - none are very popular). In those cases I'm thinking it's a current demand concern (the ironic part is, the four headphones I can think of, also happen to be near the top of the list in terms of sensitivity ) - just like cheap full-size amps and 4R speakers. Regardless, a cheapo-deluxe OTL is not something I'd want to play around with.
I will say that I never found the 701 "additionally harsh" with pure SS amps; they did nice with the CI VHP (which is TPA6120 based). But I could certainly see someone wanting to warm them a bit (EQ, amp, whatever). I know Music Hall has a hybrid based on that same chip, forget which tubes it uses - might be worth looking at in addition to the Lyr (it runs around the same price), assuming you want tubes in the chain somewhere. Would drive basically any dynamic headphone out there with ease too.