Could we have beaten the Soviets into Berlin? Yes.
Should we have beaten the Soviets into Berlin? No.
There was no reason except for bragging rights that we needed to take Berlin. The city was in the Soviet zone of occupation so there wasn't much of a point in sacrificing tens of thousands of American lives. The Russians did the bulk of the fighting against the Germans (7 out of 8 German Army casualties in WWII were inflicted by the Soviets) and tied down the vast majority of the German Army.
Now I don't think the Germans (not counting the die hard Nazis) would have fought nearly as hard for Berlin if it had been the Western Allies attacking. They fought to the death against the Russians because they were trying to delay the Russians as long as possible to allow as many civilians to flee westward and because they knew what the Russians were going to do when they took the city.
I was a commander on the Berlin Wall when it fell, and before the Fall, I would have argued that yes we should have beaten the Soviets to Berlin. After the Fall, it sure looks like Ike was right, but I still think we should have tried .... your logic is sound.
Yes, but we took more prisoners. There was a reason for that.