If some company’s alcoholic beverage doesn’t get approved, you wouldn’t say “finally some faith in the firearms system” just because the Bureau of Alcohol, Tobacco, Firearms, and Explosives handles both.

That doesn't make them part of 'the patent system', you could overhaul the patent system without ever touching on trademark law.

Logically, legally and organizationally they are separate systems. There is zero indication for overlap between them to the degree that it would warrant more trust in the patent system because someone's trademark application failed.

They are. I got a Registered trademark for one of my companies (®, as opposed to ™).

It's a huge pain (and pretty much requires lawyers, but you can do it yourself, if you are a masochist), and, in retrospect, not worth it. I suspect that why most companies use ™.

What extra benefits do you get?

Basically, the only real benefit, and that can be significant, is that it greatly strengthens your case, if going after copiers.