Tube amps "require" a transformer to get from the few-K impedance of tubes down to the few-Ohm impedance of speakers.
Crystals (transistors) conduct current far better, can drive speakers direct, OTs are expensive, so most domestic transistor gear skips the OT.
The big exception is PA. If the speaker lines are short they may be run at 8, 16, 32 ohms. But the lines may be hundreds of feet. I have a 500 foot line in REAL BIG (0.2" conductor) wire, thousands of bucks, about 0.8 Ohms round trip. If I ran that to a 4 Ohm speaker I'd lose 16% of my power. Using more affordable wire I could lose half my power.
Material costs tend to suggest a Line Impedance near 100 Ohms. That keeps copper not-huge and also acceptable insulation costs. For larger powers this leads to High Voltage and More Rules. Therefore amps 15W to 70W will tend to have a "70V" winding, making line impedance 333 to 70 Ohms. In other cases, nominal 25V is the limit, making 15W-100W line impedance 41 to 6 Ohms. Both taps are usually provided, and only a transformer can churn the same power into two very different impedances.
A SS amp can be designed for any impedance. High impedance suggests high voltages. But 40V transistors are far cheaper than 40oV transistors; and current gain must be reduced to get the hi-volt rating. Even with a transformer to give the final impedance, SS designers will usually design in the few-Ohm range, because the transistors are readily available at good price.
So the basic PA amp could be a transformerless 8-Ohm job stolen from the Hi-Fi division, plus a transformer to get the higher impedances used in long-line PA work.
All non-tiny audio amplifiers work push-pull. In tubes, since we don't have P-type tubes, and usually need a transformer anyway, we use the OT to combine the push and the pull. This is possible with transistors, and you may find one. But since 1970 there has been much work in transformerless push-pull transistor amps for the Hi-Fi world. These reached high performance and elegant designs. So the PA OT is not tasked with combining the push and the pull, and has no CT/split winding for that.