I don't think the min wage should be raised to $15 immediately, but I don't think it leads to entitlement.
Doubling labor costs instantaneously would not give businesses enough time to reasonably work the expense into the budget. Now, especially, is not the time for such a drastic and immediate increase.
Ultimately markets where the minimum wage is higher adjust so the benefit is null. There's a reason the cost of living in states like CA (which has a higher minimum wage) is higher. I have out of state relatives that say I should move because the cost of living is lower there. But so is my (realistic) earning potential.