"Remove all items that can be "stolen" from the maps and let everyone rely on the current random loot system for whatever remains. Are you satisfied with the level of character progression that is possible at that point? "
I can only speak for myself, but I've never had a problem with character progression at that point. I normally *don't* steal anything unless it's specifically required for a quest objective (the mortician's journal; 'evidence' against Esmerelda, etc), or even loot the in-town barrels and crates that are free to take things from. Despite that, I haven't had a cash shortage.
Granted, I'm also not trying to buy every single skill book the moment I see it alongside everything else that might theoretically be useful (tools, ingredients, full gear outfits, etc); I may buy one or two cheap level 1 skill books along with a magnifying glass, but that's about it.
At that point, you don't really need to steal anything to get started - there's enough stuff lying around before reaching and just beyond Cyseal (as well as in the tunnel beneath), and none of it involves theft.
If you just have to fully upgrade everything on every character as soon as you arrive, then yes, you'll probably have to resort to stealing, but that's a play style choice, not a necessity.
