It has nothing to do with open source, it's about security. Installing an app with no connection to anything invites lots of people to build apps that steal your stuff (sure this app might be trustworthy, but not all). Every Mac and iOS developer has the same requirements. Installing an app with no signature is asking for people to get hacked. Do you leave your house open so that some contractor you don't know can enter your house and do whatever they please? $99 a year means Apple can trust that they at least know who the contractor is. There are people who want to steal your stuff (or your mom's) much smarter than you or I. This isn't an onerous requirement at all. I shipped my first Mac app in 1987, back then security was not an issue. It is today.
It really is for some developers. $99 goes a long way in some places, and not everybody has a credit card either.
Also, how does paying $99 mean that Apple “knows who you are”? It identifies you as somebody willing to spend $99, nothing more. I bet that’s not a problem at all for many bad actors.