I agree that the over-friendly "hey, let's engage!" style is annoying. It feels like a sales tactic hidden under a patronising wrapper. But I do like that the emails provide a human touch. Someone has put a bit of thought into them and there seems to be a real person at the other end. In that respect, I think a middle ground is probably best - a short, friendly welcome with maybe a confirmation that we won't email you again unless you ask.

Incidentally I also like adding [Non-urgent] in subject lines for mails that can safely be ignored, but that's just my personal preference.