When I started doing street, not long ago (around 2008) I enjoyed pushing Tri-X to 1600, and I dared doing that shameful abuse with Rodinal.
For years... I just felt back then, if the image is fine, it will survive.
As some other forum members have said, as years go by we often test that great film in different developers, and at different exposure indexes.
Tri-X is wild and breaking at 1600, intense at 800, workable at 400 and superb at 200.
I like it the most at EI250 in Perceptol, with the Hasselblad and tripod. It shows its beautiful "contrast distribution" full of personality even when it receives that good amount of light, and even if the current version has smaller grain, yet the film has a strong grain presence, but that grain is so incredibly beautiful in Perceptol 1+1 and 1+2. I didn't like it that much at 1+3 or stock. For 35mm without prefocusing, I have not seen better Tri-X than EI250 in Perceptol 1+1.
But for common MF and 35mm fast overcast photography with good DOF (nearly two stops more!), I prefer Tri-X at EI800 in D-76 stock. Grain is not dissolved at all, and general image sharpness is great, just like the bite in highlights compared to 1+1. As Lachlan and others have pointed, that's not a real push for soft light.
The magic of Tri-X when we do the same scene comparing it to other ISO400 films, is Tri-X seems to mix, in some middle grays areas, a bit more low and high values details than, say HP5+, so it's very dynamic visually speaking, and makes our eye like it better often, if we do a comparison. HP5+ is more real, and Tri-X more a new slightly graphic world.
IMO it's different from Kentmere400 and Foma400 (both grainy), but sometimes Delta400 can look close to Tri-X.
Again IMO, the film is not optimized for EI400: it's only that it can be used that way, but with a bit more contrast and grain, and less resolving power than we get at 200-250.
Real pushing, say to 1600, makes it totally lose its best grain and fine detail. Both TMY and HP5+ give better pushed prints from a purely technical point of view, though the pushed look of Tri-X looks classic and works well for small sized printing.
It's totally amazing to me how it resolves very fine detail at EI250 in Perceptol 1+1: how can Kodak do that, with present grain at the same time? I have not seen any other film do it...
Lovely.