?

not necessarily.

TAS gives to stache early game to afford Pea badges, as far as I remember. And you would still sell a lot of stuff and get mush badges, although later in the game. So investing in stache some of the time is probably good.

But I don't know what the current run does and what the most up to date route is.

That's interesting, guess I'll watch it lol.

iirc giving boosts to the same stat makes it a lower chance it get 3s and 2s. Is it known how many times you have to give it to a different stat to reset that counter?

I have no idea how it works. It's different between JP and English - JP starts giving you only 1s and 2s fairly early, whereas you can keep getting 3s for a long time on English.

It's probably not a counter, just dependent on how much boost you already got for a given stat at a given level. You can get 4s (maybe even 5s and 6s?) if you never upgraded a stat until level 10ish.