I agree that junglers should absolutely not be able to get clears that are healthy and put them on an early level lead at the same time. What made the new jungle work originally is that monsters were much more significant threats, and thereby forced most junglers to lose a lot of health during their clears, while often clearing slower too. Ganking was therefore a much riskier endeavor, and ganking from full health required the jungler to head back and then head straight to lane, falling behind on experience in the process. In the current state of affairs, junglers can afford to gank practically non-stop, because when they do eventually fall behind from lack of farm, they can abuse catch-up experience to negate a significant part of that tradeoff.
Personally, what I think would help would be to turn off catch-up XP until after the laning phase, in addition to making earlier clears harsher. Fighting 2v1 all of a sudden, or even 3v2, presents a huge disadvantage at the earliest stages of the game, and that is a point where jungler needs to be the most counterable if they are to not feel oppressive. If they ganked with a stark deficit in either health or levels, that would at least give the illusion of agency to the ganked player, because they'd feel like they'd have a shot at going for an aggressive play, or turning around while retreating in an attempt to punish the jungler for going too far in. By contrast, when a jungler is the same level as you and at close to full health, there's no reason to do anything but run in most situations, and jungling as a result becomes much less engaging for everyone involved.