Think of it this way:
You are the sole owner of your account. A check made payable to someone other than you doesn't belong to you and thus does not belong in your account. That item belongs to someone else.
The size of a bank doesn't really matter. Banks might catch that and kick it out because it's not yours to deposit. Your mother could in theory call the check maker and say she never received the check. Check maker sees the item debited from their account. Check maker disputes this with their bank and learns that the account was not deposited properly. Chase would be obligated to remove those funds from your account.
While the scenario above likely won't happen to you, policies like this are in place for a reason. It exposes the bank to loss if they don't catch it and kick it out. Even if it clears tomorrow, that check can technically be disputed for like 2 years or some shit.