While I’ve never seen a simulation or study that eliminates the first inning, essentially every study you do see highlights the top 4 spots as being the most productive. A big part of that is they obviously see the most plate appearances.
John Dewan (of Baseball Prospectus and The Fielding Bible) in 2006 promoted the traditional view of best hitters batting 3rd and fourth, with the caveat that the third spot go to the faster hitter. The prominent new method (new in application, but actually pretty old) is the Markov model, which has the best hitter hitting second to maximize plate appearances. This model also recommends the pitcher bat 8th (which I don’t like) and the best base stealer bat 5th or 6th ( which makes a ton of sense to me). Why risk stealing in front of the better hitters? Steal bases in front of the hitters less likely to string together singles or hit an XBH.
And no one has ever found any way to justify the notion that protection in a lineup works.
A lot of this can be found via simple Google searches. Admitting it’s not always the most exciting reading...