cooked sauce with a "bit" of acidity (vinegar, lemon, lime whatever) will last weeks-months-years.....
If you just blend up some fresh ingredients without cooking them, think of them as a blendered salad. If you chopped up a bunch of chiles, some onion, bit of garlic (all fresh vegetables) how long do you think they would last in your refer? 3-4 days?
A cooked sauce with a bit of acid will last as long a fermented sauce. Both would potentially have a similar low pH, and would have the same longevity based on that low pH.
How long it takes to get to that low pH? With a cooked sauce....30 minutes. With a fermented sauce...7 to 90 days depending on your preference.
Both sauces are great choices, it's up to you how long you want to deal with the sauce. Wait for the ferment, or cook it up now. The tastes are sooooo different between the two styles of sauces, there's no way to say one is a better choice. It's totally up to you which taste you like and want to do.