It's not about being incapable in terms of storytelling, but about incapable in terms of combat animations. They'd need to make a whole new set of combat animations for a one-handed character, or one with a prosthetic, as long as the replacement doesn't work exactly as a natural hand - and then, again, what would be the point of losing it in the first place? Then consider that there are five combat classes (warriors and rogues have two variants), which multiplies the set of animations further.
I'm not saying it can't be done, but the probabilities are stacked against it. Unless they decide to give the Inquisitor a cool new superhand with built in extra badassery. As much as liked having the Anchor, I wouldn't like that one bit, because it would most likely be all about combat, i.e. completely boring.
My original point was not about the prosthetic, but if you insist on debating about the practicality of its use at a gameplay level, lets talk.
Let us assume we actually do get something as advanced as some sort of Lyrium Based Prosthetic (which should be considered a best-case scenario at a game play only perspective). DA4 is still 3 or 4 years down the road, I would be absolutely shocked if Bioware didn't already intend to alter the combat and its animations again (they have done so every game) in order to improve the game-play. In fact for them not to update their combat mechanics would be a remarkably bad decision at business level since they do need to stay relevant in an ever growing Western RPG market. For them to base combat around a new prosthetic or a missing limb would be no different than creating a different new set of combat animations for a new PC.
Also, the responses I'm getting on here regarding a prosthetic (that was not the focus of my original argument) are strangely lacking middle ground, especially from the Anti-Inquisitor PC crowd. Why in your mind must the arm be either as functional as the missing limb (which your right would defeat the purpose of the handicap) or be so dysfunctional that it removes the PC from a potential return? It could be a powerful tool and still dysfunctional. While I'm sure there are better ideas, the mechanic Bioware used for the Anchor in "Trespasser" could suffice as a base around this principle. The arm could malfunction in combat. The arm could straight up break and need repairs. The Inquisitor could occasionally flinch while using it, slowing them down. These are just a few basic ideas that could make the player feel the pain of the Inquisitor fighting with something new and potentially painful to use; and at the same time make the Companions more relevant to combat. Upgrades to the prosthetic (based around a weapon crafting system similar to Bianca) could help alleviate some of these negative side effects later in the game.
As for the regression of level ... At a setting standpoint a LEVEL is only representative of a characters proficiency using a preferred combat style, character level (and talent trees) don't actually exist in the world. If they need to learn a new combat style or re-adjust everything they knew in order to facilitate a new tool/limb than of course they would drop in level, because they are less proficient in how they fight. As for skills (even if you're a mage) you still would have to re-teach yourself how to use those skills in regards to that new required tool/limb, because you are now simply incapable of using them the way you used to. Stats are a better point, but the Inquisitor did lose an important physical part of their body and even stats like Magic, Willpower and Cunning again only really refer to how efficient a character is at utilizing those stats in regards to their preferred combat proficiency. Since the arm would be new and the Quizzy is still trying to learn how to use it properly, then mental stats would take a hit just like physical stats would.
The solution then is simple. The Inquisitors starting stats would be reduced, but not as low as they would be at lvl 1. Stats would grow slower (as they realistically would using a prosthetic) and if combined with a "dysfunctional arm mechanic" (that allows for improvements over the course of the game), the Inquisitor would simply hit harder (but more unpredictably) early game than your traditional new PC. Late game (with the lower stat growth on a higher base) and the ability to improve the prosthetic, the Quizzy would naturally balance out. Ending up with perhaps slightly higher stats than they had in Inquisition, but an arm that still has a small chance of malfunctioning or causing pain (if greatly reduced from how it started).
Again though I'm not using this argument in support of a Inquisitor PC (while that is my preference), but instead am using it only to show just how bad the argument of the missing arm actually is in regards to whether or not they should return.