Our internet is slow, is it the old router?

We have a router that is about 10 years old.

Our internet became very slow about a year ago and I think it is the internet company trying to squeeze more money out of us. I saw there is a lawsuit for a different company about just that very thing.

The service guy gave us some story about there being much more internet traffic now and the old router is slower, but a new router would help. I don’t understand why a new router will help? The router is just for my house to provide 4 wifi lines. How does that have anything to do with the speed of the internet?

Moreover, the internet traffic has not increased that much in one year. Bullshit. This is the most densely populated county in Florida. It’s already jammed with people and internet lines a year ago. Any new lines would be a minuscule percentage increase.

I thought I would ask the collective if there is any validity to my router being at fault. I get my internet through cable.

Only answer if you know the technology. No guessing please.