There are two main elements offhand to Concentration spells though:
1. Concentration spells can be disrupted through a DC from damage, and
2. If you have a Concentration spell running, you can't have another running.
You could probably dispense with #1 without impacting balance much, so long as you still had #2.
Thank you for bringing up this crucial and important point.
That damage breaks concentration is very bad news for, say, the Ranger that had hoped to maintain Hunter's Mark in melee.
But it is an interesting check on full spellcaster awesomeness.
The other part, however, condemns dozens upon dozens of spells to nonuse and oblivion.
The solution is NOT to lift the restriction (either in full, or the second part only) since that would only mean the Wizard would cast two of the best-in-class spells she's already casting.
A much more interesting solution would be:
Step 1: Identify at least one, preferably dozens, spell(s) that optimization guides rate poorly and that you never see used at your table.
Step 2: Add "rings of concentration" and similar magic that allows you to use those spells (and only those spells) even if you're already concentrating.
Specific rules language to follow; this just the general idea.
The ideal would to allow you to combine one buff that is currently rated red or purple, with another buff also currently rated red or purple.
You should not expect to combine any buff with one currently rated blue or gold, since that would be a direct power-up.