Yes, if Hold Person requires concentration, it can be disrupted by hitting the caster while the spell is active and force her to make a Constitution saving throw.
In this specific case, there's nothing ill-advised about having a Wizard apply her proficiency bonus to such save.
First of all, it's not all Wizards, but only those who chose to be proficient in concentration, which means they must have given up another skill proficiency.
Second, the proficiency bonus is useful only if someone actually attacks you, so your investment in this skills depends on whether your foes will make it matter.
Third (and this is specific for this spell only), Hold Person already grants the target one chance per round to end the effect. Easily disrupting the caster could make the spell too weak. But I guess there are better spells to think about in comparison.
We'll see how it works in practice, but it's even possible that the concentration rules have gone too far. If after a while everybody's tactic is going to be "attack the caster" because breaking concentration has become too easy, then we'll notice.
There are worse spells, as you note. Dominate Person doesn't allow a save beyond the initial one. The ONLY way to break is to force that check or make it that the caster is killed/incapacitated. Further, as it's a WIS save, it's very likely that your target will fail the save (even if he has Advantage), if you target Fighters, Rogues and the like.
So you've changed a guy over to your side on the fight, with perhaps a 15-40% chance of failure, and now the only way to make you stop is to kill/incapacitate you, or make you break Concentration. Any hit of less than 20 points of damage only requires a DC10 check - with your proposal, you probably have a 15% chance to fail - especially as relatively few attacks in 5E are likely to deliver more than 20 points. Even being hit for say, 30 points, it's only DC 15, and you will still succeed, more likely than not (a barrage of small hits is the best way to break concentration, barring a giant one - but the latter may well kill the caster anyway, so that's win/win I guess).
Making Concentration into a skill is a terrible idea on other levels, too - for example, it takes away from the RP and other-pillar elements of skills, making you less able to engage with them, in favour of more combat power.
You say "not all wizards", but here's the thing - any caster interested in using CC spells or powerful buff spells would be pretty foolish to neglect a +2 to +6 bonus to their Concentration check. The only casters who wouldn't want it would be those who weren't going to use those spells anyway.
I don't expect we'll see anything like this, though, fortunately.
EDIT - Also, if you think making people not hit the caster is the goal (which seems very questionable), then making Concentration a skill does not help with that. It just means people want to KILL the caster or take him out of the fight with hard CC of their own, rather than just hitting him hard enough to break his spell. If anything, it makes casters more of a target.