I feel like Thaumaturge is the worst possible example here, tbh, because having two actions of setup on every enemy and then not even getting to trigger your martial mechanic twice when you make your two attacks sounds really lame. Barely even functional even.
There are much better picks if you want to highlight how strong poaching Flurry-like mechanics can be.
TBH this whole tangent is sort of pointless but you brought up other classes using the stronger unarmed strikes. Anyone but a ranger using Twin Takedown is going to be questionable because no other class has as strong an incentive to hunt prey. A better example would probably be Double Slice. A Thaumaturge (or whatever) could much more reasonably go for something like:
Turn 1 Exploit, Stride, strike
Turn 2 Enter stance, Double Slice.
Turn 3 whatever, Double Slice
You'd need two archetypes, though, so without free archetype you wouldn't see it before level 8 so it isn't much better than going for Flurry of Blows at 10.
Actually, though, flurry of blows and double slice would stack. If you want to do pure damage on a monk, double slice + flurry would be probably be the top way to do it, which is boring.