Colour developers work by producing dyes in the film via colour-couplers so the neg should have the same stability and permanence.
Where the trade-offs will occur is in things like film speed, grain, contrast, colour accuracy.
You can get monobath B&W developers but they suffer in these areas too.
If they were as good as 'regular' developers then we wouldn't bother with 'regular' developers.
They are OK if you are in a hurry or doing something non-critical though.