The problem is that feedback loops start to kick in above 2°C so it doesn’t matter if the economy crashes.
In fact, in some cases that makes things even worse. One example is that without smokestacks and ships pumping out sulfur dioxide the albedo of the atmosphere will rapidly drop, which might cause immediate and rapid warming over a period of only a few years.
We could be pushed past 2.5°C or even 3°C without industrial forces contributing at all.