Ah, but it was not until the invention of the pentode ("e" being the fifth letter of the alphabet) that the transmission trajectory really took off. Numerous valve vendors repackaged their pentodes as tetrodes (a smoke-screen, especially if you took the screen above its rated voltage). The pinnacle of this technology was reached with the 807, which forced the anode to move to the top of the envelope (whence the term "pushing the envelope"). The "e" particles were never higher than in that fine component's plate cap.
All kidding aside, many years ago I had an RCA audio theater amplifier that used four 807's in AB push-pull-parallel. It was awesome.
E.g., around the time De Forest invented the triode, Reginald Fessenden was inventing AM radio. "AM" stands for "amplitude modulation", wherein you vary the strength of a radio signal to conform to a wave form from an audio source.
Fessenden's solution to the modulation problem was admirably brute-force: Generate a radio signal using a really fast (and heavy) alternating current generator and modulate the generator's output with a water-cooled carbon microphone!
In 1904, he got his alternator from General Electric. It was a 50kw model, designed by Ernst Alexanderson, operating up to 100khz. It was more powerful and a lot quieter than the spark-gap contraptions he'd tried earlier (with limited success, however). And, on Christmas Eve, 1906, it sufficed to produce the world's first AM radio broadcast.
De Forest's invention paved the way both for better ways to generate RF and better ways to modulate it.