NYSP normally does not operate within incorporated areas (re:cities) unless invited with the exception of state facilities. That is not to say that there are not units that operate with other agencies / task forces etc. in cities. The simple reply to your post is you are correct to a point. Many times the "troops" just use the home agencies frequencies / radios as they are frequently available and many of the home agencies are unaware of what radios are available outside their own system. The average "radio buff" (not derogatory) being better versed in what is out there does. Not a perfect world, and that is just a tip of the iceberg when it comes to radio systems and politics.
Not to mention Troop NYC is very small and mainly consists of investigators and Recruiters (from what I have seen). Also I believe they operate on whatever system(s) that Troop L is on.
New talk group 6031 with surveillance on it. There is actually a lot of NYSP activity in NYC, Narcotics Investigations, SIU, Auto Theft, ESD, VFW, etc.