"Your Medallion membership entitles you to enjoy unlimited complimentary upgrades, subject to availability".

In this context, "availability" does not mean an empty seat in F. It means an empty seat in the fare bucket DL allocates for UGs (V or X). How many seats DL releases for UGs is based on how many are already taken, and how many they think they might sell based on historical data. SFO-JFK is a heavy premium market, so they will likely keep a number of seats open in hopes that they will sell them instead of giving them away.

If you use a tool like ExpertFlyer to check for UG availability, you'll see that on city pairs with several flights a day, UG availability can vary greatly (for instance, early morning and late afternoon/early evening flights favored by business travelers will typically have less UG availability than flights at other times of the day). While it's not impossible to get a UG a day or two after the GM UG window opens, if you don't get UGd at the window, you have little chance of getting UGd until 30 minutes before.

Also, keep in mind that even if 12 F seats are unoccupied, there could be 12 (or more) PMs who haven't UGd yet, or GMs/FOs on Y fares, who would all be ahead of you in the UG queue.