Well remember, the Masters events starting opening up from Big Four dominance in 2017. But as you say, even before that, in the height of the Big Four Era, the stray Masters wins tended to happen later in the year. If we count the Fedal Era, non-Big Four Masters went to:
2005 (Fedal Era begins): Paris - Berdych
2006: Hamburg - Robredo, Cincy - Roddick, Paris - Davydenko
2007 (Djokovic's first big titles): Madrid & Paris - Nalbandian
2008 (Murray's first big titles): Miami - Davydenko, Paris - Tsonga
2009: Shanghai - Davydenko
2010: IW - Ljubicic, Miami - Roddick, Paris - Soderling
2011: All Big Four
2012: Paris - Ferrer
2013: All Big Four
2014: MC - Wawrinka, Canada - Tsonga
2015: All Big Four
2016: Cincy - Cilic
2017: Rome & Canada - Zverev, CIncy - Dimitrov, Paris - Sock
etc.
So it really broke up in 2017, but as you say, Paris in particular was often won by someone other than the Big Four (or super-elite). TO put it another way, of the in the 12 years of 2005-2016, there were:
108 Masters events.
92 won by the Big Four
16 by other players, 6 of them Paris, and 8 of them after US Open (Paris/Madrid/Shanghai).
Here are the number of Big Events won by the Big Four, by year from Roger's first in 2002 to Novak's last (so far) in 2024 (bold is all big titles):
1, 2, 7, 11, 11, 12, 14, 11, 11,
14, 14,
14, 10, 13, 13, 9, 9, 9, 4 (of 7), 5, 5, 6, 1, 0
That's a lot of big titles! The Big Four collectively won
at least half of every big title in each year from 2004 to 2020, and at least 10 in every year from 2005 to 2016. The collective peak is obviously 2011-13, when they won all but one big event - Paris by Ferrer in 2012.
