Rightly said, sir. As I mentioned earlier, we practiced this policy before.
Anyone who intended to take leave was to write an application, which was approved 99% of the time (the 1% was only when too many people were taking holidays at the same or a similar period). We used to file those applications, but honestly, tracking them was difficult.
Negative Aspects of Open Leave Policy
We were not able to track contingency leaves. Many people just called or texted their HOD about not coming due to health issues. This went unreported, making it difficult to determine the actual number of leaves availed (also, we don't have a punch card system; we use traditional muster attendance).
People who seldom took leaves for genuine reasons were not recognized because of the inability to track things down.
Certain people were able to enjoy as many as 30-40 paid leaves a year, while there were a few who never availed one and were never appreciated for it (lack of tracking).
The company was not able to punish frequent leave takers for two reasons:
a) No maximum leaves per year were declared.
b) As mentioned before, difficulty in tracking leaves.
As a result, when I joined as HR here a couple of months back, I reframed and designed the leave policy to a maximum of X leaves per year. Sure, people may take advantage of it, but once they know they'd be rewarded for not availing those leaves, they'd think before taking leaves casually.
Hope it helped :)