I'm not sure about that - you're not solving a problem, you're simply moving it. Currently there are 2 decisions to make - whether the ball hit the arm, and whether it was deliberate. In the vast majority of cases, even if you can't tell if it DID hit the arm it doesn't matter because you have no indication it's deliberate anyway. And judging whether it hit the arm is, IMO, one of the trickiest things to judge. If the player's body is oriented to yourself in an unfavourable manner, then a ball striking the chest will look like it his the arm sticking out to the side.
So, you're not making fewer incorrect decisions with the change your proposed - just making different ones.
But then again, there are a lot of scenarios where the law, as stands, doesn't really work. Player tries to control the ball with his raised thigh and it skims off to his arm, what to do about that? One problem with your law proposal is that you're encouraging attackers to deliberately kick the ball into the arms of a defender - and you ARE going to miss it when it does happen. But the incidents with the arms sort of by the body and being struck with the arm are so grey anyway, that may that change still has more positives than negatives.
Sometimes, of course, it will also be difficult trying to judge whether a 'benefit' (let's call it that rather than advantage) was gained - a shot is taken, accidental handling, then goes out for a corner - if you can't tell if the shot was on target, then is the handler benefitting or not?
Personally, I think if nothing else, it needs to be written to something like 'handles the ball - or permits the ball to strike the arm - when the player could otherwise reasonably have been expected to be able to avoid such contact'. 'Deliberate' is too highly misunderstood by both players and referees (how many referees have you heard say they carded a player for 'deliberate handball?')
Oh, and the 'backpass' law needs to cover all body parts. Want to keep the game flowing? Stop heading, kneeing etc the ball back to the keeper. The current law makes no sense. Gets rid of this absurd notion of 'circumventing the LOTG' as well (I'd be amazed if any other sport has anything that ridiculous)
Although if they want the game to flow they really should introduce a time restriction on how long the keeper is allowed to hold the ball. I propose 6 seconds as a reasonable timeframe.