Maybe there's more sentimental employees at TWC than we realize.
I'm sure there has to be a legitimate business reason behind delaying cutting off the analogue feed other than that enough people at TWC are "sentimental" about the legacy STARs. This is a large country with a huge number of headends, and, even with plenty of advance notice, chances are not everyone's going to be ready for such a major change. Given the choice between meeting its deadline but losing viewers or quietly extending the deadline in the hope that those headends that haven't caught up to modernity yet eventually will, TWC would much rather retain viewers through the use of antiquated equipment.
I'm sure not every headend operator can easily afford to upgrade to new equipment to keep up with the rapidly-changing times, and The Weather Channel usually isn't at the top of the list of priorities for where a headend's money should be spent. If money were no object, then
every headend would be equipped with an IntelliStar 2. My cable company is currently in the process of upgrading to an all-digital signal, years behind some of the bigger players in the cable TV field. And there are plenty of cable companies smaller than mine that are lucky to still exist, basically.
