Overcooking and oversteeping your tea releases extra unwanted tannin. This is what makes the bitter taste. This can be hard on an empty stomach and for people prone to nausea.

High presence of tannin lowers the absorption of iron:

https://www.cambridge.org/core/journals/british-journal-of-n...

https://academic.oup.com/ajcn/article/106/6/1413/4823172

It also increase the oxalates:

https://www.urologyofva.net/articles/category/healthy-living...

All of that being said, many people aim for teas high in tannin for the taste. There are also studies that will show the potential health benefits of tannin. As with many things, moderation is probably the answer.

Yes, your teeth will fall off!

Jokes aside, the longer you leave the bag in, the more bitter your tea will be. You also get more caffeine. For a lot of tea connoisseurs it destroys the taste of the tea. I say try taking it out after 3, see if you like the taste more or less.

You can also re-use tea for a 2nd or 3rd brew, but that's not possible when you leave the bag, the 2nd batch will come out too light.

This is more important if you have good tea leaves. When you steep too long, you get the bitterness and the sort of "dry" mouth feel.

You might be using weak tea. Buy some good stuff (I recommend Barry's as an excellent black tea, the gold blend is really good) and you will absolutely want to take the bag out. If you're drinking Lipton, well, stop, but if you have to drink it you might as well leave the bag in.

It's all about taste. I find green tea to get bitter after a few minutes of steeping.