In not so recent (2015) study Flat Design vs Traditional Design: Comparative Experimental Study [researchgate.net] scientists measure the performance of current and past interfaces styles. They reference multiple past articles and studies (some freely avaliable like Ref 3 [belveal.net] or Ref 11 [cooper.com]) so they are not walking new ground, just measuring some more.
Some interesting background:
The density of screen information [in flat design] is often extraordinarily low .
The main criticism was that flat design ignores the three-dimensional nature of the human brain, which is extremely sensitive to visual cues linking interfaces to the real world. The removal of affordances from interactive interface objects means that users regularly perceive interactive elements as non-interactive, and non-interactive elements as interactive.
Despite these limitations flat design is becoming more and more common, and criticism of experts in HCI and usability is generally ignored by the software industry and graphic designers.
They used different tests: finding a word in text, finding an icon among others and finding clickable objects in a webpage. The process included eye tracking and recording of mouse motions. Subjects were students below 30 years old and already using similar interfaces, so effects in older or disabled persons were not studied. Font tests showed similar times, but worse cognitive load (derived from eye motions) for flat style. Icon tests showed worse times and mental load for flat style, a more complex task pushing the brain out of semiautomatic mode. Webpage tests were also against flat style, with high miss and false alarms indicators.
The conclusions were clear:
Our experimental study supports the opinion expressed by many HCI and usability experts that flat design is a harmful tendency in area of user interfaces, and should be replaced by interfaces based on the design principles developed over decades of research and practice of HCI and usability engineering.
Now we have more proofs that "flat design is inferior to traditional design", we aren't just whiny users opposed to change that don't understand what is going on. Based in personal experiences, and those of older persons around me, my conclusion is that any "UI/UX expert" that keeps parroting the modern interfaces is just a fad-following graphic designer at best (I expect more from those too... but they keep on disappointing me), and in any case should not be allowed into the HCI field. There were other studies, and this one is around 4 years old, so maybe it's time to get back into saner styles. Not that I hope things will improve fast after realizing that since this study things have slided more into simpleton mode.