Just looking at it from a physics point of view - hang a weight (moment) off of a steel rod (member) - there are already known effects on how the steel rod will behave in motion. See engineering and physics textbooks, modeling software, etc. How much or how exactly the behavior will vary though I guess is a different story and is probably where the debate arises - then add in other factors such as user error, different barrel profiles, etc.
Can't find the time stamp right now, but there were about 60 seconds windows in this podcast that summed it up pretty well IMO:
This episode Caylen invites a special guest as a subject matter expert to discuss the hot-topic item of barrel tuners. Aaron Hipp is an accomplished PRS competitor with over a decade of experience in the sport competing at a high level. Aaron’s background in education and occupation is...
moderndaysniper.podbean.com
On the flip side, I imagine Litz would know all of the above as well - so I'm kind of curious how he arrived at his conclusion of tuners generally doesn't make enough of a difference to matter.