I think that as a method, Petrus is a good method, especially for teaching beginners advanced techniques. As a speedsolving method I don't think that it has the ergonomics to keep up with the other methods. 2x2x2 is fine (see xcross) as are the last 2 steps (right block and ZBLL). The main problem with it is the ergonomics and lookahead of expanding to 2x2x3. I'd argue that intuitive RUF is worse than intuitive RUL in many cases. As far as the EO step itself, I don't see it as a weakness or advantage.
Imo, LEOR is a better Petrus alternative. The steps are FB, EODFDB, RB, ZBLL. The last 2 steps are the same and the first steps are pretty much equal (it's slightly on the side of petrus by 1 move). The biggest difference is that you can see EO in inspection (if you're good), as you do EO while solving the 2x2x3, not after, and the expansion to EO2x2x3 is all RUMr (with controlled Fs in certain situations) and rotationless in comparison to the LUF > RULFM y'. The movecount is pretty similar (maybe the same), but the ergonomics are just better for LEOR. I also think that it is definitely competitive with the "big 3" and certainly has some aspects that make it more attractive than CFOP, Roux or ZZ, but also some drawbacks like any method.