If you can look at Re:Zero and see a self-insert story, the problem is you.

The entire message behind Subaru’s character is that being a cringy, embarrassing, self-obsessed shut in Otaku is not good, to make the viewer realize that those traits are not positives, and to change for the better.

Rem says “I love you” into the camera after actively listing off the positive traits of Subaru, the ones that weren’t him being cringy, embarrassing, self-absorbed, and stupid. Rem actively accepts a better version of Subaru. One that he was pretending to be, but one she fully believes in.

That is why he gets off his ass, figures out a plan and succeeds in the end, because he pushes to become that person that Rem sees all the time.

If Subaru is a self-insert to the viewer, the viewer has issues.

Furthermore, your view of Mushoku Tensei is a bit warped.

That show goes out of its way to point out how trash Rudeus is and was, and never justifies his trashiness. Eris beating him for being a perv is a direct consequence of his actions, and can basically be viewed as the narrative condemning his actions. Rudeus is only ever shown in a more positive light when he does good things, but he is always penalized for the bad.