That's largely what did happen in 1944. They conducted the Vyborg–Petrozavodsk Offensive from early June 1944 to mid-August 1944. The Soviets put nearly a half a million men up against roughly a quarter million Finns. The campaign all but broke the Finnish army, led to the resignation of President Ryti, and multiple offers for a negotiated peace.

However the Soviets paid a heavy price for that victory. The numbers are not consistent between sources, but it is clear that the Soviets suffered between 100,000 and 200,000 casualties, and several times as many casualties as the Finns. Moving on to Helsinki and finishing the job wasn't going to be a bloodless operation. The Finns had proven to be a very capable opponent, especially on the defensive. The priority was Berlin anyway. So the Soviets negotiated a peace where the Finns gave up all the lands they wanted, basing rights, and a large war reparations... and just as importantly the Finns promised to fight and expel the German units left in Finland. Finland wasn't reduced entirely to a satellite state like say Romania, but it was placed firmly in the Soviet sphere.

No reason to waste another quarter million men to fully subjugate Finland, when they could get 90% of their goals with no further loss of Soviet lives. Those instead were spent reducing Berlin.