Or has it remained a terminal node at the frontier of mathematics?
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Oakley and Baker's 1978 paper The Morley Trisector Theorem describes very nicely how Morley came on this result "from above", meaning that he had a much more complicated result of which this theorem was a particularly nice special case. (Such a trivial case, in fact, that Morley didn't consider it worth publishing.) So even from the beginning, this theorem was not an investigational endpoint, but more of a beautiful side comment.
Oakley and Baker's paper also mentions that "Morley's theorem has connections with many notable point-line-plane-circle-polygon configurations bearing such names as Apollonius, Brianchon, Ceva, Desargues, Feuerbach, Hesse, Lemoine, Menelaus, Pascal, Ptolomy, Simson, Spieker, Steiner, etc.".
Morley's theorem is from 1899(†), and 110 years later, in 2009, we see a very nice and very short paper by Brian Stonebridge, A Simple Geometric Proof of Morley's Trisector Theorem. It was not 110 years of silence, either — the Oakley and Baker paper alone gives 120 references! As Stonebridge appears to be unaware of Alain Connes's proof mentioned above, apparently there is currently no single complete list of proofs — no terminus, as it were.
(†) according to Stonebridge, Wikipedia, Cut The Knot, and others who categorically date it with no discussion. However, both Coxeter and Oakley and Baker appear very knowledgable about the history, and they are more vague about the date, hinting at something maybe around 1904. Since Morley didn't publish it, but merely slowly started mentioning it to friends, it is difficult to date.
I think any of us would be happy to have people still working on our theorems over one hundred years later — Morley's theorem is not and never has been a terminal node!