Multiple concerns: it will only forward emails as long as the acvount is alive. Google recently annoinced it will close accounts that are inactive for certain time so if you stop using it and just use it for forwarding you are risking to lose the mail. As well there is the privacy concern that google reads every email of yours and by forwarding you are not really solving that concern
I just did this. I have an android phone so I will have a hard time getting rid of google account but I have used clodflare to create a custom email and have setup forwarding/sending vianalias inside gmail. I made a separatr address for website registrations and personal mail. I will slowly start the transitioning of all my accounts.