How often do you think someone tries to connect their gamepad to a local server? Not never, but the total amount of users doing it is probably high tens or low hundreds at most
Compare that to how often gamepad users try to connect to a malicious website - probably hundreds or ever thousands of times a day.
Loosening certificate validation further expose the many less than competent users to risk, and the potential impact both on the customer base and on the product's reputation are significantly higher than the risks of making it cost a couple bucks a year to allow your gamepad to connect to a local server.
For something like a computer, there is a legitimate argument for allowing the user to bypass SSL/TLS restrictions (after some resistance) because laptops are used for development.
I can almost guarantee that the gamepad developers had an options for certificate validation bypass in it's developer options, but they're not gonna expose that needlessly when it offers no benefit, but exposes their customers to additional risk. Your gamepad is likely not a development device after all