My guess would be that the issue wasn’t that the cards weren’t being played often enough, but that they were being played too often.
There are a veritable plethora of ways to increase your Counting the Days quality (see here). Most of them, however, are either opportunity cards or require you to belong to a particular faction or have a particular quality.
My guess would be that most people didn’t bother with them, and used the Acquaintances instead, as using the other method is a pain for most characters (unless you’re a Master Thief who’s sold his soul and is aligned with the Bohemians/Great Game) so all the work adding these options to a bunch of opportunity cards was wasted. Moving the Acquaintances to an opportunity card puts all of these options on the same footing.
And, sure, if you’ve already gone through this cycle as many times as needed to get your Iron Republic Safe-Conduct (and, if so desired, the flavorful but not particularly useful Consonant Violin), then any change to–or even complete removal of–the Counting the Days system or Acquaintances is largely irrelevant. For those who still need or want those items, however, this change made that task a lot more irritating without any real compensating benefit.