There is no reason to send a non-boilerplate cover letter to a large company, especially given the fairly high likelihood that it's either processed by a machine or discarded entirely. The lack of transparency about what happens to cover letters is even more discouraging, so maybe you should put a little note in your careers page that you prefer no cover letter to a boilerplate one.

On the other hand, if it's a small company and the CEO/CTO/Hiring Manager is <firstname>@<companyname>.com, then a meaningful cover letter that's not more than 2-3 paragraphs has a good chance of getting a response of some kind.

In my most recent job search, all followup came from going to events, meetups, or hackathons and gaining contacts that way. I figured out that spending 3 hours a day trying to compose meaningful cover letters could be better spent going to events talking with people, although this is only an option for people in certain cities.