HOMM came out a year after Commodore's bankruptcy by which point the A1200 & A4000 were quite old (and AGA was underwhelming to begin with). There is a recent port of HOMM2 though.
Most PC games could've been done on the Amigas of the time, depending on what spec you were targeting. One of Commodore's very many mistakes was that they had never had a product that sat between cheapest, base-model Amigas and the ultra expensive big-box pro models.
An Amiga 2000 was something like 4 times the price of an A500 and offered nothing for a home user, not even a faster CPU. The Amiga 4000 did, but again it was mega expensive. To get better performance, they forced you to for a load of pro features that meant nothing to a gamer.
What if they'd two or three models of A1200 at the same time? For a couple of hundred quid extra they could sell you a higher-end A1200 with a 68030 or 040 CPU and plenty of FAST RAM. It could've run Doom quite nicely and that would be the model that every gamer would crave (and probably end-up saving up for). That might have bought Commodore enough time to turn the company around. This kind of What If-ery is a popular past-time in the Amiga community. There's never a shortage of braindead decisions to talk about.