Disclaimer: I haven't worked in a wet darkroom and so all of this is from theory.

Not really.

The enlarger itself was a rather simple setup. It also works with a rather shallow depth of field (though one tends to stop down 1 to 3 stops from wide open to avoid aberrations in the enlarger lens (depending on the lens itself)).

The depth of field in the enlarger isn't that deep. Its deep enough that allows for the curvature of the film surface or irregularities of the easel/baseboard... and possibly enough that you could do some shift corrections in it to get things that are slightly askew in the film to project correct on the paper to within the depth of field's acceptance.

However, the adjustments for various lens aberrations would be so minute that it becomes impractical to do so... and it would only be viable with a single camera lens / enlarger lens combination. With this in mind, some aberrations might be correctable (for example, spherical aberration might be). However, nothing will help you if you're doing an 8"x10" contact print because there's no enlarger there.

Things like chromatic aberration (which is not impossible to correct in the digital darkroom) becomes nearly impossible to correct in the traditional wet darkroom. Other aberrations such as coma and astigmatism (my nemeses) involve significant remapping of the light on the image plane that its just not at all practical (bunch the paper up here... and stretch it there? or a very precisely crafted set of lenses to compensate for a single lens).

Philosophically, there's a different approach in the wet darkroom vs the digital one - work with the constraints of the media. Yep, you've got lens aberrations - so put them in places where its not noticeable, or stop down when necessary. You aren't trying to make The Perfect Image For All Time and you acknowledge that there are many forces well beyond your control that are just things that you need to accept. You couldn't go in and fix every silver crystal to be just right (pun intended). Its an art, not a science and the flaws are part of the art.

Related reading:

• High-Quality Computational Imaging Through Simple Lenses

"[The complexity of modern optics] is required in order to compensate for the geometric and chromatic aberrations of a single lens, including geometric distortion, field curvature, wavelength-dependent blur, and color fringing.
…[W]e propose a set of computational photography techniques that remove these artifacts, and thus allow for post-capture correction of images captured through uncompensated, simple optics which are lighter and significantly less expensive."

Note that bit about modern optics - one might be able to make a lens that corrects for a specific lens (not a zoom), but it would involve some very complex glass. I'm also going to point out that the enlarger lens is typically much larger than the camera lens and thus more likely to have aberrations of its own (though they tend to be very high quality lenses) than the lens for the camera.