You make an assumption here that the software is also constant or static.
> There's a constant low-level flow of "we switched from X to Y and got Z% speedup" articles on HN, and while the details of the articles are often quite interesting, with rare exceptions I find that I read them and conclude that it was an error to ever have used X in the first place and the team should have been able to tell immediately that it wasn't going to be a good solution.
The language X was probably a good solution at first. Then the company started to increase its product surface or acquired enterprise customers. Now you have new workloads that were not considered and the language is no longer suited for it.
Most likely a decision is made to not introduce a second language to the company just for these new workloads as that complicates the architecture, not to mention hiring and managing, so you stay with language X and try to make do. Now you have language X doing more than it is suited for and response times often increase due to that.
This isn't really a case of startup growing pains, just that software itself cannot know ahead of time every application it'll have. You can choose a "mostly fast for all use cases" language and bet that your applications will fit those general use cases, this means you win small but also lose small.