Why Hire Adventurers?

[KorvinStarmast]

In the OPs context of goblins, the idea is clearly that the goblins are attacking lands that have established human settlements, and which should be protected by the same infrastructure used to resist invasions or deal with rebellions or brigands, in a 'fringes of civilisation' context it basically means the villagers are encroaching on the goblins rather than the other way around, and in such a context the village is the bad guys.

Nope. That village doesn't exist in a vacuum. Likely origin of it is a charter by a nearby lord who is trying to increase that amount of land under cultivation. That's how a lot of places grew: push back the edges of the wilderness and increase the amount of arable land under cultivation.

Do they work for rice? and/or beer?

The Seven Samurai did (in Kurosawa's wonderful film)

Plausible Deniability is certainly a reason not to use regular military forces. It's one of many.

Regular military forces in feudal/medieval period is a bit of a backward pushed anachronism: the 'regular' were available usually for about 40 days per year. It's a limited resource, not the always on regulars that we see in 20th and 21st century nation states.

Can't muster the peasantry for a serious fight because it's right in the middle of harvest season, pull six hundred peasants or even minor nobility

This is related to my point above.

Also the new lord of NextDoorShire is paranoid about you because of your relationship with his uncle who just tried to usurp him and will definitely notice if you muster troops and march towards his border.

Yeah, the politics of it is another wrinkle that may call for
"... get me these temps to do this thing for me - Castellan, just how much does this Eau Noir group charge for such services, anyway? Let's make a deal that allows for some deferred compensation...summon them to my chambers as soon as you can track them down..."