You're right that score voting does better in that simulation when everyone votes honestly. But if everyone votes strategically, then score voting and approval voting are the same. (This makes sense because tactical score voting is mostly just score voting with maximalized votes, which is basically the same as approval voting.)
Using approval voting basically forces everyone to use tactical voting. Which might be less good in some metrics but it ensures that all voters have basically the same amount of influence, as opposed to tactical voters having more influence than honest voters. I think having equal influence is pretty important.
I'm not sure if this simulation that everyone likes to cite has been run more recently with STAR voting. That would be interesting.
(One of the reasons I prefer approval voting over score voting is that there's less of a gap between strategic voting and honest voting. Everyone is forced to give a maximalized yes/no vote for each candidate rather than casting a lukewarm vote.)