To be clear, while the TWA hotel is physically connected to JetBlue’s current T5 (via one of those super cool concourse tubes that are shown in “Catch Me if You Can”), it’s connected landside (as @raines noted, there’s an elevator near the JetBlue baggage claims if you follow signs for the TWA hotel–I’ve used it as a shortcut to get to the taxi line at T5).
It’s a fully functioning hotel with guestrooms, a gym (that outsiders can pay to join), ballrooms (my kid went to a bar mitzvah there a couple months ago), etc., so it’s not really practical to have it be airside and require every hotel guest go through TSA.
Note also that at JFK the active terminals aren’t even connected airside (although I think the future T6 will be connected to T5).
If you do have a long layover at JFK, I definitely recommend exploring the TWA Hotel over hanging out in a boring airline lounge. The food and drinks at the hotel are nothing special, but the spaces and the displays are great fun. If you have a really long layover, bring a bathing suit and check out the rooftop pool with views of the runways (open all year round–it’s heated in the winter). But allow plenty of time to switch terminals (if you aren’t flying from T5) and to clear TSA (regardless of what terminal).
