AGPL does have restrictions, and it's anyone's preference as to whether they're good or bad, but there has never been an intent to forbid businesses. If anything it's the recent RedisLabs' modules license and the SSPL-style licences that do it: they explicitely contains the wording to indicate that the product can't be used to create a similar product and offer it as a service. Heck, the SSPL says (https://www.mongodb.com/licensing/server-side-public-license):
"If you make the functionality of the Program or a modified version available to third parties as a service, you must make the Service Source Code available via network download to everyone at no charge, under the terms of this License"
The AGPL tells you that if a user asks for the source code, you must give it to them and them only. The SSPL says that the source code must be publicly available to all, at no cost. It was created specifically to prevent competitors to run MongoDB as a Service. Surely if they had to change it's because the previous license did authorize competitors to do it. Wanna take a guess what the previous license was ?
The AGPL doesn't prohibit starting a business, it makes starting a business prohibitive.
Look at all the SaaS offerings of MongoDB (formerly AGPLv3): https://news.ycombinator.com/item?id=19362919
AGPLv3 doesn't make starting a business prohibitive, arguably forks like NextCloud would not exist if AGPLv3 did not compel codebase users to publish the additional code they wrote to extend OwnCloud