We have done many, many skim coatings over textured walls....Only problem is that they will never be perfectly smooth. They will have the 'illusion' of being completely smooth, but if that wall is 'smack-dab' in front of serious downlighting or a sunny window...there could be some wincing on your part...
So this method is ok, but it has some limitations. FWIW-most of the walls that we skimmed were in basement areas, thus not highly visible.
On the other hand.....if you want to do the job right and be able to look at it on a bright sunny day and not cringe, then you should gut and re-do. I am not saying that it can't be skim coated and come out right....to cut corners...you could try it. (FWIW - When we do skim over texture - we stiplulate in our contract that there are no guarantees for perfect smoothness)
1.) This is the least costly method: Skim over to a smooth surface. If you go this route, make sure that you find someone who actually knows how to do this and has done it before...
2.) Costly: Go over the walls with new 3/8" sheetrock. Attach these with long screws into the studs. You would have to bring out all window and door jambs to match...also an extra expense.
3.) Most Costly: Gut and install new sheetrock.
4.) Another alternative: Skim coat over like what was discussed earlier and then add a layer of different texture. Like 'orange peel'....it covers alot of minor imperfections. Examples: