the easier solution is just to move funds to a new address and then anyone watching you doesnt know if its still you or someone else you made a payment to.
Yes.
For most users, this is all that is necessary. And some users improve on it slightly by sending the big chunks to multiple smaller chunk addresses, of random "payment" sizes, at different times. And they generally avoid reconnecting them. Experienced users also recognize the benefits of a reliable and
anonymous poker site where BTC can be deposited, and different amounts later withdrawn to different addresses, with no fees.