There are a number of private mooring buoys at the small private island in the San Juans where we have property. Of course, these are in salt water so have different problems than a similar setup in fresh water. We use one of these buoys when we visit the island.
In terms of using them, there are no cons that I can think of other than having to dinghy to shore instead of stepping to a dock.
The cons if you want to consider them as such have to do with inspection and maintenance. In salt water the buoy line/chain arrangement should be inspected every year if possible. Carey and I broke a buoy line at the island when we were rafted to it and the wind came up---- the upper link of the galvanized chain had worn and rusted to the point where it broke, releasing the shackle and the short stainless chain that connected the anchor chain to the mooring buoy.
The moral here is to make sure everything---- anchor and anchor line/chain--- is sized and strong enough to hold your boat in any winds you can anticipate with a significant safety factor. In the case I mentioned above, it was the two boats jerking on the chain in the waves that the wind humped up that exceeded the remaining strength of the chain link. Had the same wind come from another direction where it would not have pushed up waves, the weakened chain probably would have held us.