Deleting spammy backlinks - is this really good advice?

I run a 14-year old news site concentrating on global residential real estate. We have about 350,000 uniques/month and make about $5,000/month gross from the content. There are maybe 20,000 pages on the site.

Someone I've been talking to is always telling me I am losing backlinks. He says:

"You have over 300,000 backlinks but all of them originate from just 6,000 domains. But it’s not only about the good links [i.e., they are not the only ones that matter] but the bad links too.

"The site needs a massive cleanup that will involve going through the site's massive amount of pages and disavowing the spammy links, 301 re-directing the good links that go to pages that see no traffic, and evaluating the links that add no link “juice” for pages that see very little traffic."

This seems strange advice because all our pages have massive amount of internal linking. So even if "juice" is going to pages that see little traffic, it will be circulated to other pages.

I can imagine disavowing spammy links might make sense. But, really? We never did any link-building in 14 years. So how much damage could unsolicited links be doing? If it was a major problem the web would be crawling with SEOs promising to kill opponents' sites by over-burdening them with spammy links. I don't see these "destruction pros" around, so I imagine spammy links don't matter so much, unless they form a pattern which Google judges is a result of a link-exchange scheme. But absolutely no-one fears us enough to have artificially simulated a link-exchange scheme just to hurt us.

So is my advisor correct?

Likely unnecessary. Maybe if spammy links made up a vast majority of your total links. Might be worth checking if any pages in particular have a large volume of spammy links.

If something aint broke, don't fix it. Disavowing will show google that you think there is a problem when there isn't. You have no penalty, traffic is constant.. don't sweat too much.

Leave it be. Google will simply devalue any spammy links. This is why many times you will see websites with large amounts of spammy links get smashed when an update rolls through (out of whack ratios of quality vs spam links). Negative link velocity (lost links/decay/devalues) is a thing and usually why I see sites lose rankings (not the other way around). I'm sure over the last 14 years, you've seen some wild fluctuations in traffic after updates, especially ones that are heavily Penguin related. This is almost always due to the above. At this point, don't even waste your time with disavow files and 301 redirects, etc... Your website has the age and authority already intact and I'm guessing the good links outweigh the bad, which you see a lot with older aged authority type websites with the type of traffic you are getting.

tl;dr - Don't waste your time.