Because it infects code even if you don't modify it. You could just be using an API of an AGPL service, and it will hit your code. Its universally banned not just startups. I don't know of any organizations that allow it in their code base. If you want people to use your code, don't AGPL it.
How about this: There are AGPL software vendors who think making HTTP requests to their AGPL software forces you to license the client as AGPL too. To avoid their lawsuits, companies forbid internal use of AGPL software.