Okay I went and did some research.
I tracked my opponents for 100 battles, with 98 wins and 2 losses. I did take a 15-20 min break after battle 78, which may have affected the dataset as I had less repeats (only 2) when I came back. All battles were the 3 trophy/highest offered fight.
Of the 100 fights I was offered a player I’d already fought in that set 21 times. The closest together and shortest time being offered (just 12 minutes) was with River Song as battle 32 then again on 36.
13 players appeared twice.
2 players appeared three times.
1 player appeared four times (Sister at battles 2, 48, 62, and 100 (sorry bout it)).
Beyond the dataset’s scope I marked 68 of the 100 matches as people I’d already fought this week in my current total of 1,115. So one can argue that variety is definitely lacking to some degree. 
Thoughts for future:
I should’ve tracked who was revenge/rival to see if they were being offered more often than regular players because they were triggering as revenge/rival.
I should’ve tracked the guilds to see if I am being offered Top 10 guilds over others on the board. I definitely fought a LOT of Anonymous players this week.
Would’ve been fun to track what teams/troops I fought to see how they stacked up (but I thought of that too late into the process)