Fighters can't learn Healer base lists, not even at the Restricted cost, because they aren't the right realm (and can't be, because those are hybrid lists). If a fighter wanted some magical healing ability, picking up the open channeling list Concussion's Way isn't too bad (7/10), but the closed list Blood Law would be 15/20 so that's a minimum of a quarter of your DP every level you purchase it. And it's not as good as the Healer list (for a fighter, the subconscious casting ability of the Healer lists would be pretty huge).
Whether other base lists are available as Restricted lists is a GM call. Personally, I would be hesitant especially for an Arms character. I might limit the number of lists to be taken that way, or disallow it entirely.
It's generally true that any character can max out their weapon OB ranks (although the lack of a professional skill will keep them from matching OB, and typically stats won't be as high either). For a Healer, that's 5/7, not prohibitive although it will cost you some versatility. The advantage of a Fighter is usually in their hits (but Healers are an exception there) and in the expertise skills. The Fighter is going to be able to get away with attacking while moving, with multiple attacks, heavy armor, etc etc, and they'll also be able to have more OB skills (e.g., they can also fight at range, and maybe unarmed, or get full benefit of a shield). The Healer needs to invest a lot of points in their defense (shield skill, armor), so probably in the total scheme of offensive-plus-defensive capability they are going to fall short on one side or the other. Only looking at OB overlooks that.
Pastaav's point about comparing total DP expenditure is also pretty important, since that's the measure of how much versatility you are giving up.