It's not just the price, though. Selling, say, Super Mario Bros. for $5 would be bad enough, but Nintendo has been forcing people to buy the same games over and over again because there's no way to move them to newer consoles when they come out.
(I could be wrong about this. If so, please correct me.)
No you're right, but a lifetime license to software on all platforms is a losing proposition for any company, since there are non-trivial costs to re-releasing on new technology.
Also it may be easy to link digital purchases right now, but proving past cartridge purchases would be very difficult.
They actually got rid of exactly that. You cannot buy Super Mario Bros. on Nintendo Switch. You can only subscribe to a service that contains Super Mario Bros.
(I could be wrong about this. If so, please correct me.)