Standing water on a green isn't good for playability or turf health. In theory, if the water is able to freely flow off, we should never have "bird baths" on a putting surface. However, over time a combination of bunker sand, topdressing sand, and organic matter can accumulate on the perimeters of greens, which can act like a dam.
In order to address this, we need to do some targeted aerification on the small areas which are preventing the water from leaving the green.
This clearly isn't a one and done procedure, but takes an on-going effort to prevent these areas from getting worse. And in some extreme cases we will break out the sod cutter and shave these spots down slightly to alleviate the issue.
So if you happen upon some holes in the collars and surrounds, you now know why they are there.