Price Gouging helps on both managing the demand, and resolving supply.

Demand

• Normal person - You don't particularly need gas. You don't own a generator, and you have nowhere else to go. If gas prices are $3, you will go stock up just in case that's the normal price and you know it'll be hard to get soon. If gas prices are $10 or more, you will just wait until prices come down. Maybe next time you store an extra gas can just in case.
• Small demand - You have a generator and burn through gas to keep niceties going. If gas is $3 and plentiful then you'll happily burn it to keep AC on. If gas is jacked up to $10, you will ration your use and only keep on the fridge and lights. If prices raise too high to $50, you won't buy gas. These prices naturally ration your use. If prices are too high, next time you might have bought a more efficient generator instead to save money.
• Critical Demand - You have a mission critical use for gas, and are running low. Maybe you're keeping people alive with hospital care, or keeping critical services up like servers/bloodbanks/etc, or saving lives with gas powered equipment inside the affected area. You will pay up to $50 for this gas, and at this price almost nobody else will buy it but you. Next time, you resolve to keep more gas stored locally.

Sometimes, an area won't be hit that bad hurricane and won't see too much increased demand. Other times, an area will be hit very very bad, and rarely places will need to allocate gas to only critical demand from the start.

How can you make sure gas sometimes gets to critical demand, and other times only gets rationed slightly or not at all? Freely set prices solves this automatically, while rationing needs a whole fucking algorithm to resolve (which might not even be something that people on the ground can check). Rationing also always disincentivizes at least one group on the ground to not prepare for next time (eg, if rationing is per person, then average people are disincentivized from keeping gas cans. If rationing is 100% critical, key institutions are disincentivized from storing because gas stations become their personal backup storage).

Supply

• $3/gal - This is the normal price. You have no bidding power to ameliorate the problem. You will only start to get gas once the roads are cleared. Even once cleared, trying to deliver to you sucks more than normal, so you will get LESS gas than usual, prolonging the crisis.
• $10/gal - This is a high price. You have slight bidding power. As soon as the roads clear, you're first in line because you can pay a premium to get priority on gas delivery or more deliveries to clear up the suppressed demand. You will get gas FASTER than normal, resolving the crisis faster. Next time, you spend the extra to make sure your station is topped up before the storm.
• $50/gal - This is a 'gouged' price because the crisis lasted longer than expected or you have even more critical need. At these gas prices, you can resolve issues NOW. Maybe you contract an offroad fuel truck to coming driving over even with fucked roads. Maybe you can pay to airlift fuel in. Maybe you hire people with ATVs or pontoons to ferry fuel canisters if things get bad enough. No matter what, at a high enough price, people will find a way to resolve things. Next time, maybe you'll take your profits and spend a lot of money on doubling your storage, so you can earn more money.

Sometimes, you can wait for gas supply to be resolved naturally, other times you need to exert a little more effort to fix things, and rarely you need to make extraordinary responses.

How do you know when you should spend extra money to do this? Solving it requires an entire government agency, and as we saw in Katrina that agency is shit. Gouging is messy and not everyone prices optimally, but they are highly motivated so they try what they can think of and the problem gets fixed eventually as the market finds what is most efficient.