It happens in game development when you're targeting resource-constrained hardware consoles.
It can happen in web development as well if you're working on a disciplined backend team that cares about designing for request latency and concurrency.
But often scrappy startups don't have the time or money to care about those things. It's more about product fit and keeping customers happy to keep the money coming in.
I personally don't use that excuse and design everything I can with a budget in mind. It's a nice constraint to have an upper bound on response time. Forces you to pick your battles.