The problem with this line of reasoning is that it implies the business exists to serve the software. Unless you work at a tech-focused non-profit, the software actually exists to serve the business.
Sure it does, but the business also wouldn't exist without the tech in Ubers case (and a lot of other cases). And it's going to be your head on the line when you keep adding these 100ms sentences because the business wants it for no good reason and your page takes 3 seconds to load, and nobody buys anything from the site.
More common is a "death by 1000 cuts" scenario where the various causes of slowness are apparent to the developers, but quite difficult to remove because they've become necessary to the continued success of the business.
No, I'm questioning whether the value added is greater than the value lost, and in this hypothetical example clearly not. So it's your job to point that out to whoever and not silently obey.