Tom
There could be a number of different reasons for the poor drainage. Some have already been listed and it could even be a combination of factors.
There is no real chance of getting an accurate diagnosis on an internet forum. It would need to be investigated properly by someone experienced in turf and soil. Anything being posted here is simply a guess.
I would suggest that if cut cups in fairway areas are still full of water, the problems is probably deeper in the profile and unlikely thatch related unless your thatch levels are 200mm deep. The cup should be bypassing the top layer so if the problem was at the surface the holes would not hold water.
Regarding no aerification for long periods, I have seen many courses that have probably never performed any aeration ever and they drain fine. The appropriate renovation schedule is determined by many factors such as climate, soil type, grass type, nutrition an water inputs, traffic etc.
If you have a concern, a chat with your super is a good start. There may be constraints he has to operate under that limit what can be achieved. The next step may be for your club to look to an agronomist for further advice.