For TK, I use them for Asia to US return and haven't had a problem getting a suite before. Even when travelling as a family of 4 or 6 in J, there has always been at least 3 rooms available.

I would think the only way for TK to avoid dissapointment is to clearly state which flight connections are eligible. A simple web-based tool to type in flight number or PNR would be the first step, even better if it shows how many rooms are free at the time. And other options such as Tour Istanbul or Hotel eligiblity. I remember the first time I took TK, I spent an hour trying to find the Tour Istanbul desk.

With how much space there is in the airport, adding a dedicated area to lie down / lounges / sleeping pods dosen't seem far fetched. Althought since TK re-used the old furniture I'm assuming budget for lounges is really tight.