Outputgap -- that 1964 list is like every rollcall I ever said 'Anseo' to in school 
I know a few Marys who are now 13/14 (in the US). I think it's a timeless classic.
I would say the Irish leader thing is partly due to there being so many of them the chances are many Irish women of a certain age will have a certain name or a certain set of names Mary, Catherine, Margaret, Bridget, Anne, and Elizabeth are all very solid names in the 1964 list that could have been passed down a few generations and were very popular for many years. Maria and Marie are also in the top 100 for 1964 so the theme was popular.
In some families or maybe even regions, families adhered to a tradition of naming children in order of father's parents, then mother's parents, then siblings or aunts/uncles or great grandparents, etc. You wouldn't be guaranteed that a first daughter would be called Mary, but given its long history, you might see a good few. There are none in my mother's family, which is a bit odd perhaps, and the name only comes up as a second name in my dad's, and in the case of one aunt who was given my gran's name backwards.
In 1964 you can see Caroline and Jacqueline going strong thanks to JFK.