But there is nothing obvious about this? For one, this is speech that can only be done using otherwise regulated means. You couldn't claim "free speech" and build a radio tower that transmits long distances, as an easy example. For that matter, you can't claim free speech to allow concerts at your house. You similarly could not claim free speech to rent or loan out rooms of your house for storage.

As has been pointed out elsewhere, if you want to take the effort to connect and verify the different parties that are going to communicate with your server, you are almost certainly going to remain free to do so.

Do I think there are probably some concerning ways those burdens can be placed on folks? Certainly. But we already require inspections and other similar activities for things that individuals can do at home without an inspection. See the food industry.