Mounting the enlarger to a counter is very common. Attached is a shot of my (current) darkroom that shows my DII mounted to a corner-counter.
DII's require a lot of head room - in my current darkroom I took care of that by building a recess in the ceiling above the enlarge to allow the head to move all the way to the top of the column.
In my previous darkroom I had to deal with a low ceiling. The solution in that case was to mount the enlarger on a shelf attached to the wall, and then made the counter top below the enlarge adjustable so that I could lower the easle to increase enlargement after raising the head as far as it would go.
Prior to using the DII, I used a Durst F60. That was also mounted on the wall shelf. The only time when it makes sense to have a baseboard that is a distinct part of the enlarger is when the setup must be portable.