I've written about this several times, if briefly (not here, I've just given this thought).

If you're reading fansubs, you're absolutely right that there can be too much information. It's a blessing to read the proper definition of a word, or find out that "boy's day" is a real Japanese holiday. It's a curse because the screen *really* starts to require attention.

Since most standard (non-fan) subs don't include all that info, it's seldom been an issue for me. The subbing included in most decent productions are much more natural, and can be effortless to follow. I can also read fast, so that helps.

Still, I do wonder when I know a foreign word in a language and then don't see it written down (or its possible slang use). I think meaning may get lost sometimes because some things aren't actually translated.

If you know Spanish, you know how often things get left out. It must be a billion times worse in Japanese. Apparently, the actual translations of some episodes titles are, basically, poetic...

There's a big problem (with subs) that you missed though: when they're not timed right, subs can mess up a moment. You find out the end of a sentence, and its important info/impact, while people are still at the beginning of the sentence! It could kinda kill the climax of a powerful reveal, or the rhythm of a scene.