For 2, the system is just broken. There's no balance between a message that's acceptable in terms of time to be able to send for a user (say, 10 minutes of proo

For 2, the system is just broken. There's no balance between a message that's acceptable in terms of time to be able to send for a user (say, 10 minutes of proof of work), that would reduce spam. If someone sends me a message every 10 minutes the service is unusable, but making the proof of work more expensive means it's unusable as well. This is why the original proof of work for email was broken as well.