Well, I tried that with an amp I once called the Aurora. SE input, and if memory serves, the conversion to PP prior to the driver, which was PP. The problem is the input tube has a high output impedance, which enormously complicates the transformer operation.
You see, the input transformer of the new amplifier, as well as the Mark I Karna’s, is driven with a low source impedance ... the preamp. There are a handful of ancient preamps with a Zout of 8k or so, but they are hard to use because a Zout that high makes them very susceptible to rolloff from cable capacitance. Most tube preamps have cathode follower outputs in the 400 ohm range, and if feedback is used, quite a bit lower. Transistor preamps can be as low as a few ohms.
Transformers like to see a low impedance on either the primary (input) or secondary (output). It doesn’t matter which end. The problems start with an interstage, where the secondary is driving a grid, which has a near-infinite impedance that is somewhat unpredictable, and a primary connected to a plate. The nicest sounding tubes tend to be the old octals, or even the true antiques, the five-pin tubes from the Thirties.
They all have pretty high output impedances, 7.7 k or higher. This is a really high impedance for a transformer. The lack of bandwidth wasn’t a problem back in the day, since AM radio bandwidth was never higher than 8 kHz, optical movie soundtracks the same, and shellac 78’s were mostly noise above 6 kHz. And program sources didn’t go lower than 50 Hz. Modern bandwidths of 30 Hz to 15 kHz didn’t arrive until the mid-Fifties, with magnetic tape, modern LP’s, and FM radio. By then, transformers were used for line level applications in studios, and for output transformers in power amps. This was the all-analog vacuum tube era, of course.
Interstage transformers are a very special use case. We are reviving a 1920’s and 1930’s technology to modern high-bandwidth applications, but there are still limitations, mostly the result of using high impedances. I did use what I call "Interstage 1" in the Karna amplifier, but that was really putting the transformer right to the edge of what can be done. Adding phase splitting to its task list means I will likely see phase spread at the top of the band due stray capacitances not matching between sets of windings. This is a solved problem for studio line-level transformers, but asking interstage transformers to do this results in a not-very-good interstage transformer.
And frankly, for what benefit? It isn’t like a SE input tube is all that awesome. In phono preamps, sure, SE circuits make things easier, what with RIAA compensation combined with noise considerations. But for the input stage of a power amplifier? Where’s the benefit, except for tradition?
So I restrict phase splitting to the easiest location, the input, where it isn’t doing much else. This is proven studio technology that’s been around since the 1930’s, and well-refined by the 1950’s. The interstage, a far more difficult task, is confined to the driver/output interface, and is fully balanced on both ends.
Yes, there are interstage transformers on the market that are SE to PP. I would not use them. It is very difficult to get HF symmetry on the secondaries, but modern transformer designers can do a lot that wasn’t possible even ten years ago. I wouldn’t be surprised to see a 300B SET driver interfaced to PP 300B outputs through such a transformer. I won’t be the one designing it, though.
A power amp with three 300B’s would have a certain visual appeal, and you could weave a fun story around it to match the visuals. At the hifi shows, you could hang pictures of famous trimotor airplanes, like the Ford Trimotor.