did anybody try comparing how fast/well students learn in Taiwan and in PRC while controlling for IQ to see if simplified characters really are of any benefit?
E.g. I am guessing that the switch to simplified characters should have “broken” a lot of the traditional mnemonics that describe characters by their components with various levels of granularity. Did they come up with new mnemonics for simplified variants?
No idea, but it’s worth noting that simplified characters are easier to write out by hand, which could make learning easier even if the meaning that can be gained from the constituent bits is diminished.
It’s also worth noting that modern characters are already simplified versions of older characters. Simplification makes it harder to see what the original pictograph might have been, but it’s already fairly impossible to tell that. So long as the child can learn that those three odd marks on the left mean water, whether it seems intuitive or not that they should mean water, they’ll continue to mean water whether drawn with three marks, two marks, or a squiggly line. As long as it’s consistent, it can be learned.
My eldest daughter has gone through the regular mainland simplified school system for 5 years. My wife, who also grew up with simplified, tutored her extensively. Mnemonics for simplified was not an issue. Note: I didn’t really pay attention to the mnemonics used though.
I don’t know of any studies but there probably are some. This is a hihgly emotionally charged issue, at least with regards to Chinese culture and the attitude in Taiwan. I learned simplified for 2 years in University, switched to a traditional enviroment (lived in Taiwan), then primarily a simplified environment. Out of 20+ years, about 8 have been in the traditional environment of Taiwan and HK, and 15 in China.
I can only tell you that from my personal experience, it is definately possible to learn both. It’s easier to have one as an “anchor” language (the one you learned and generally write with) and read only for the other one.
The pictograms and mnemonics obviously changed. One example is the character “ai” for love.
simplified = 爱
traditional = 愛
Close but the traditional still keeps the heart/心 radical. The simplified has taken the heart out of love. 
One for sheer complexity is “rang” or “to allow”
simplified = 让
traditional = 讓