On a lot of subjects, sending cold email AT ALL is pushing the envelope. It might be convenient for you to communicate with somebody, but that doesn't mean it's acceptable for you to waste their time.
Unless you have a specific reason to believe that there's been some error in the way your email was handled, or unless you have some positive right to a claim on the person's attention, following up IN ANY WAY is beyond the pale.
Yeah, unless you have some kind of prior relationship with the person, it seems extremely weird and annoying to send follow-ups when they haven't answered. Unless you work in PR and that's your job or something.
Unless you have a specific reason to believe that there's been some error in the way your email was handled, or unless you have some positive right to a claim on the person's attention, following up IN ANY WAY is beyond the pale.