Back in the 1980s, having a long-opened checking account represented a sort of stability or "credit-worthiness" when presenting a check to a merchant. If an account had been opened more than a few years before and the check number was high, the feeling was that the odds were higher of the check being good.
I remember as a kid my mom showing me and explaining that the little numbers next to her name and address on her checks represented the month and year that the account was open. She spoke of it as a badge of honor and mentioned how important it was to keep a long history of keeping a checking account active.
I also remember (perhaps incorrectly) that for some transactions checks with a check number lower than a certain threshold would not be accepted.
Given that checks can be ordered by mail or online (or printed at home) with a fake address and arbitrary check numbers, few people rely on these for any security benefit. It stands to reason that the account opening date is no different.
If that's the case, why is the date that I opened my checking account still printed on my checks?