I think this is a good, but not sufficient, answer. From a reader:

I think the main problem with the idea is that it would expand the
worldly role of the Vatican: it has taken a very long time for the
Church to get in a position where it is neither part of a secular state,
and therefore under the government’s influence or control, nor ruling
over a significant area therefore making the Pope as much a prince as
the leader of the Church. The current situation with Vatican city being
a super-tiny state with diplomatic ties but virtually no secular power
or non-clerical subjects is the perfect situation. Expanding the Swiss
Guard and sending them on peacekeeping missions would rock the boat.