If you consider over $150K on deposit irrelevant, I guess you're not my kind of bank anyway.
in today's poor interest rate environment and every bank being flush with cash, an account of $150k may be considered irrelevant to many banks, while to the account holder it would be anything but insignificant. I'm hearing of more banks going the route of depositing interest payments into a DDA or SAV account rather then send checks out, solely due to cost of the manual process of doing so. and if the interest check is small, they frequently aren't cashed and then have to be escheated down the road - all this monitoring costs money.
Many internet banks still pay a higher rate of interest than traditional brick and mortar banks, if you haven't already done so you should investigate that. Bankrate.com tracks and shows highest CD rates available, i don't see any listed over 1%, so many banks aren't really bending over backwards to service CD customers, especially if the CD is the only account in the relationship.
and please understand i'm speaking in general terms, there are many banks that state one thing and make exceptions to accommodate customers, happens almost daily.