One important reason I value speed in software is that it leaves me less time to get distracted. If I'm expecting something to take a few seconds, often that's enough wait time to prompt me to check my phone or reddit or something. Best case scenario I've just turned a 3 second delay in to a 10 second delay. Worst case and frequent scenario because I'm ADHD as fuck is that I get lost browsing.
An area where I think speed is neglected is when people are thinking about what to build. Something I see mentioned occasionally by people here, on reddit, and by friends: They'd like to work on a side project but don't have any ideas for something useful to build. Just take something thats otherwise already useful but slow and make it not slow! These days you can't swing a dead cat without hitting a web app that doesn't need to be a web app, or desktop app built as a web app. There's no shortage of options.