Except when your app is meant to be used by them for work and their IT has them stuck on an old version of IE.
I know that customer requirements are pretty much unheard of in startup land but other companies have to obey this kind of limitation in order to make any money (which again is an alien concept in startup land -- not every business model survives on growth alone).
For a lot of business owners using an old version of IE, the browser is something to facilitate their bespoke ActiveX application. They probably don't care if their employees can browse less sites.
And on the flip side, a lot of those employees are a sizeable chunk of business for other businesses when they browse on their lunch breaks or whatever. So, large sites aren't going to fully drop support for any browser until after the market share has dried up.
That's their problem. They'll install Chrome. Quit making excuses. I've heard it all a thousand times. Stop supporting old browsers today and business will adapt.
I think you're assuming that the employees in question are permitted to install software freely on their work computers, and/or that the company decision-makers are aware of new sites/services they're denying themselves by their policy.
Firstly, the policy is there for a reason -- often something like "we paid a lot in 2003 for this custom software, and if we upgrade browsers we'll have to pay X to have it rewritten/replaced".
X may be a rather large sum of money -- easily enough to overwhelm whatever benefits they might get by becoming paying customers of whoever's new venture.
There's also a potential for a sort of catch-22; new sites/services may pop up that could even replace their old custom-built software... but if they can't even try it out and the site looks awful on their browsers, a) it's less likely they'll make the jump and b) it gives the impression of being a new-fangled flash-in-the-pan sort of thing. After all, the serious companies online put the effort into supporting older browsers.