What you are describing it pretty much what mixers do. They basically take your Bitcoin and send it to other addresses that want privacy and they are sent at random amounts and random times. Is it truly anonymous? I don’t know. There are some firms that can trace it anyways perhaps.

Keep in mind if you do this and send to an exchange like coinbase there is a good chance your account might get locked since they don’t like it when they receive funds which come from a mixer. Due to AML they are very strict.