Because less than 5 is not significant and doesn't matter.

that's not base 5. That's just increments of 5... in base 10.

base 5 would be: 2400, 3000, 3300

Because it makes more sense to mark 325, 350, 375, 400, and 425, on the knobs of the oven than 307, 337, 373, 401, 421, and 449.

Because we have ten fingers.

There is no real reason we use base ten numbers except that we ran out of fingers at ten and used that as a “round” quantity. Five is a convenient half of ten (and one hand of fingers) for higher but not excessive precision. We could have developed a base eight numerical system if we had four fingers per hand and in that alternate reality, you’d be asking why cooks and chefs cook in base 4 increments.

In metric countries, it tends to be in multiples of ten (180, 190, 200, etc). In imperial, it tends to be in multiples of 25 (350, 375, 400, etc) rather than strictly 5. And that's largely because, as you've noted, that's the smallest meaningful resolution; the difference between 210 and 212 in either system is essentially random noise. Even a very good oven is going to fluctuate in temperature more than that.

Want to know something crazier, though? Before cheap and accurate thermometers, bakers obviously couldn't use degrees in recipes. Instead they used "slow oven," "moderate oven, and "fast oven" or "cool oven," "medium oven," and "hot oven"--clarified with "very" intensifiers as needed--to describe cooking temps for food.

I know yanks hate decimal and stuff because of how hard the mental arithmetic is, but it's half of the more significant digit. I guess and they wanted more precision than 10s, but don't see the need for 1s, so they split it in half or the equipment is not capable of more precision.

TBH - I don't know what a dungaree fezundheit is anyway, but I'd imagine 5F is way spurious accuracy already for a domestic oven. I reckon you'd need an industrial or scientific kiln for that type of accuracy - so it's probably more a psychology / user interface thing. In which case the answer is, 'because enough customers are happy enough with it as it is.'

There’s no way Fahrenheit ovens are more accurate than Centigrade, and they use 10s and are like half as accurate anyway