+ and the most important question here is: how does Turkey profit from being part of NATO? (It doesnt)
Well, the answer to that can be based on both objective perception and subjective perception. My knowledge of NATO rules and regulations are, unfortunately, not too sharp, but from what it appears:
* the objective perception holds that NATO membership invariably adjusts, or it should adjust, the financial burden of member states relating to their defence spending. As the defence of one NATO member is a shared responsibility of all other NATO member states they all feel confident in relying on major powers (also members) for their defence and thus reduce their spending. At least, the Americans see it this way and believe European members are relying too much on the US financial and hardware support and not contributing enough portion of their own GDP for the collective defence.
Secondly, NATO membership helps gain access to the US and European military hardware, including nuclear weapons. Needless to say, Turkey houses US nuclear weapons, which in principle were placed there to guarantee deterrence for Turkey (and of course, its neighbours) vis-a-vis the Soviet Union. Not to forget, the Turkish Air Force's large fleet of F-16 and other American fighter jets. Turkey may have paid for them with their own money but NATO membership certainly eased the transaction.
Subjective perception would hold that even though Turkey is a NATO member it has largely been left to fend for itself. NATO membership has had a little positive impact on its defence spending as well and Turkey remains largely self-dependent in this regard. As of recently, it is being blackmailed by NATO members to align its foreign and defence policies with the West/NATO without having much to gain in return.
For me, the bold points above are very important. If Turkey walks away from NATO then one wonders what state its defence and security would be left in? Will Turkey be able to maintain its F-16s and other American military hardware in the long run, especially if the US pushes for restrictions at minimum, if not complete sanctions? Already the US has pushed Turkey out of the F-35 programme. Also, will Turkey pursue its own nuclear weapons, even though there is little need for it now? If it does, is it willing to accept full sanctions by the US and Europe?
On the side note, if it were up to me I would push for a new CENTO type organization between Pakistan, Turkey and Azerbaijan. The three states have very much sensitized their foreign policies with each others'. We either support each others' international claims or look the other way if we have no dog in each others' fight. Other members should be included if they agree on the aligning their foreign policy stances with these three states, at least on the key disputes. Sensitising defence and security might be a good idea for both the collective defence of the three countries and regional security handlings. The primary task of the alliance should be to ensure collective defence and ensure that the existence of each state is not threatened. The secondary task should be to maintain a joint force able to move into fragile regional states if they fail as a state and variably or invariably threaten the safety, security and existence of the three-member states. Through this Pakistan can extend a nuclear umbrella to Turkey and Azerbaijan (controversial and problematic, but considerable). There will, however, be a powerful backlash from both friends and foes alike. The three states should see if they are willing and able to absorb it.