COH2 goes like this:
1) Make a lot of infantry.
2) If you're Ostheer, you get maxim or conspammed. If lucky, you fight some cars, which gives you lots of map control.
3) If you can hold on, as Ostheer you get 2 paks and an AC. Soviets make AT guns if their mines don't kill your AC.
4) You make Elefant in 2v2 or 2 Tigers in 1v1. If you're feeling really lucky or want to troll, hold out for Tiger Ace.
5) Soviets make ISU or IS2 or Shermans. Everyone's infantry now dies because Relic didn't want us noobs to have to micro both infantry and tanks late game, so the tanks obliterate all the infantry now.
6) Heavy tanks shoot at each other till someone wins.
I actually had a game yesterday where both me and my opponent used combined arms and doctrines without call-in tanks. It was glorious, the most fun I have had in this game for a long time. But yeah 95% of the games go like how you described it.