Broken links and SEO

While I have heard over the years broken links could potentially harm SEO I have not personally seen it. After a review I'm going to clean up some broken links today as it surely cant hurt.

Have you shown positive results by removing old broken outgoing links?

Broken Links leads to 404 pages ... If Visitors Clicks your website URL and welcomed with 404 error.

It’s indirectly increases your bounce rate — Higher Bounce rate is synonymous to little or no value coming up from the website .

With time you lose value.

IMHO — I’ve not seen a big improvement like that working with 404s ... I just honestly don’t want a dead page on my website.