There are OTL amps. Harold Beveridge actually built a speaker with a dedicated OTL amp.
I am aware of OTL tube amps, but it's like saying that bicycle tires are suitable for cars -- you just need lots of them in parallel. The Atma-Sphere S30 Mark 3.2 OTL tube amp produces 30 watts per channel into 8Ω load and needs five output tubes per channel to do it, drawing 400 watts of power from the AC lines. They are serious about requiring an 8Ω speaker, with their manual warning not to use any speaker that drops below 8Ω at any point (almost all 8Ω speakers dip well below that). From their manual:
Atma-Sphere said:
The amp will give its best performance on 16 ohm speakers. If using an 8 ohm speaker, it is very important the speaker exhibit at least an 8 ohm impedance at all frequencies. In any event, the speaker load should be one known to be easy to drive. Speaker cables can have a rather dramatic effect and you are invited to experiment.
So, technically, tubes can drive speakers in the same way that, technically, mopeds can tow boat trailers -- as long as you have enough mopeds connected to a shared trailer hitch and the road is absolutely flat and you don't mind their inability to deal well with that large, reactive load.