The big no-go for me would be allowing you access to my gmail inbox. Google is already starting to add unsubscribe links right in the email header area [1, 2]. You probably don't want to complete with them as they have a much wider insight into email patterns and can quickly come up with a much wider block list. I'm sure you take security seriously but your service would definitely be the weakest link if someone broke into your auth token database. At least, that is how I think your service works, it is not really clear, other than it works with gmail (and I'll allow you access to read emails). I'd focus on the security message here as I think this will come up a lot.
A suggestion. A proxy service might work here, where I use your service and you give me a email@leavemealone.xyz, I use that email@leavemealone.xyz email to sign up to lists, then you forward email to my inbox, then I never give you access to anything. Then this will work with any email provider and you can access way more customers.