In particular in the case of the Finns, they only wanted a limited war, but there was no guarantee that they could get it. Stalin refused to accept their recapture of the border areas, and eventually hammered them hard enough that they conceded on his terms. But even if the Soviets were willing for a separate peace, the Germans would have objected vigorously to it because it'd free a number of additional divisions to face them. That would've probably made a formal separate peace treaty a no-go from the Finns standpoint due to the risk of a triumphant Germany deciding to punish them after the conclusion of the war with Russia.
While historically the Finns were effectively stopped by stronger Soviet resistance after the opening months, changing circumstances if the German offensive went better than it did historically would've probably meant that they wouldn't be able to stall claiming the opposition was too strong. Freeing up a large portion of their army with the fall of Lenningrad - especially if it happened in early 42 because cutting the life road completely starved the city to death (the Germans came within a hair of doing so historically) and there wasn't a huge civilian population to control - is a reasonable simple proxy for when changing circumstances would result in the Germans being able to pressure the Finns into advancing well across the 1939 border.
Did you ever see history portrayed as an old man ... weighing all things in the balance of reason?
Is not [it] an eternal, imploring maiden, full of fire, with a burning heart and flaming soul, humanly warm and humanly beautiful?