To set it all straight, it has to do with thermal expansion and contraction, then also with taper contamination.
The spindle gets warm during use, which causes thermal expansion and then you stick a cool/cold tool holder into the bore that is not expanded/enlarged by heat. The tool holder being cold/cool and slightly smaller, goes just the slightest distance further into the spindle bore. Any pressure during use, like drilling with a large size drill, will tend to push it even further up into the bore. If it is on a short cycle time and does not spend a lot of time in the spindle bore, it usually pops right back out, quietly. If it stays in for a while and swells because it also gets heated/warmed up, then it sticks a little, as it swells against the walls of the spindle bore. If it warms up a lot and the spindle bore is dirty and the tool taper is dirty, then it sticks a lot. Sometimes it will not even be released and you will get an alarm and have to deal with it.
Regular simple cleaning for the spindle bore and wiping down each tool as it is loaded will almost always stop the problem. While I agree that a little grease on the pull stud is a good thing, the spindle bore is the priority. Clean it regularly.
Air cylinders are used on the Haas machines and many others. It is a cost and maintenance reducing strategy. A hydraulic release would mean that a hydraulic system with pumps and high pressure lines would be required. This raises the cost of production and would require regular maintenance and higher initial costs for the machine.
From memory, I think that the size of the piston for the release is about 35 square inches and with the air to the machine at about 85 psi, that is about 3000 pounds of force on the tool release shaft. That is plenty of pressure, applied rather slowly so as not to bang or hammer on the end of the shaft, but at times it is not enough to overcome a poorly maintained spindle bore and tool. I'm too am guilty of not keeping things clean and get a tool that sticks once in a while.
Could I, as the great genius that I am, design a better release mechanism, you bet. But they have been using the same unit for over 20 years and I suppose they are reluctant to change now.
Oh well, I'll keep it clean and keep making money!
Mike