Australia has been using a much more complicated ranked system since 1918, and Ireland has used an even more complicated weighted proportional system. The entire state of Maine adopted IRV, and cardinal systems are much simpler. It’s not a fatal disadvantage.
http://scorevoting.net/Complexity
The Approval Voting system is arguably simpler than the status quo, because you remove a rule. The one that stays your vote is invalid if you vote for multiple candidates.
extensive computer simulations show that approval voting works extremely well, especially when voters are more tactical (game the system). and it has worked phenomenally well so far in fargo and st louis.
https://rpubs.com/Jameson-Quinn/vse6