The logic is that the Half Fare Plus is just a prepaid CREDIT (for buying tickets), NOT a TICKET/PASS itself in the sense of some entitlement for using public transportation.
Therefore, the date chosen as first day of the HT+ subscription is when you can start BUYING tickets, the travel date mentioned on them is irrelevant. Also, no ticket inspector will ever want to see your HT+, as (s)he couldn’t care less about how you bought your ticket(s).
On the other hand, 1 day before the subscription expiration if there’s still some credit left, it will allow you to still buy tickets (such as e.g. Saver Day Passes) for a travel date which is several weeks or months in the future!
(I’m not from SBB btw, just a customer)