But that's taking this $10k figure at face value. Gap insurance is supposed to cover the difference in value between what you still owe on the car and what the market value is if it's totaled. How do you make the numbers come out to a $10k gap? Odds are you're not only buying a new car (which was your first mistake) but you're buying a fairly expensive new car. And you're living paycheck to paycheck.
Sorry, it doesn't add up. The general advice is to keep six months of living expenses saved up. If you have that level of savings, plus the income that allows you to spend that much on a car, you have enough money to take the EV-maximizing route. Otherwise, you're being financially irresponsible spending that much on a car in the first place, much less on -EV addons like gap insurance.
In any case, what I said still holds: if you can afford to bear the variance, you're still better off maximizing your EV.
(Another EV-maximizing tip: whenever you're offered an extended warranty, instead of buying the warranty, take the cost of that warranty and put it in a separate savings account. If something you own breaks, use that savings to repair or replace it. They wouldn't sell the warranty unless it was profitable for them. If you sell yourself the warranty, not only will you have the money set aside for your stuff, but you'll get to keep the profits as well.)
if someone is unlucky the money they set aside from this wouldn't be enough to cover the costs of repair / replacement. Warranties are similar to insurance, in that risk can be spread out over the pool of customers that bought the warranty. As long as its unlikely that a customer will have to use that warranty, a warranty can be offered for a price that's much less than the average cost of repair / replacement.
If you're the only one contributing into a warranty / insurance pool, risk isn't spread out at all. You might end up being fine, but its also possible that a lot of your stuff will break at once, and you won't have the money to replace everything. That might be unlikely, but you're still taking a personal risk.
To some people, the value of peace of mind is huge.