If society collapses and recovers relatively quickly, we likely can coast for 10-20 years on the computers that have already been built. This would be what I'd expect to happen with a point-in-time catastrophe that disrupts everything but then ends and we can all set to work to rebuilding everything. (Like a massive economic collapse, huge meteor strike, nuclear winter, etc.) Even if 95% of computers become inoperable, there's a lot you can do with the remaining 5%. Probably more than what you can do with new stuff you build.
Another scenario is that we recover really slowly. This would be due to some kind of enduring factor that holds back humanity, like a really long-term famine or global political instability that we somehow cannot reset. In that case, what's the hurry to develop software that's ready to go? Maximizing compute capability doesn't seem like it would be the thing that tips the scales and allows society to get rolling again. For that you need to solve whatever the root problem is.
TLDR, if we fall, maybe there is nothing holding us down, and we can bounce back up relatively quickly, in which case we don't need this. Or there is something holding us down, then it seems unlikely that computing is what we need to solve that.
Maybe there are other scenarios that I haven't thought of, though. Or ways that computing would help in the above scenarios.