As your question implies, batting Aaron Judge leadoff is an odd choice, but batting someone like him at the top of the order is not unheard of these days, although it certainly is not the norm. As you indicate, in a traditional lineup, Aaron Judge would be placed in the third or fourth spot in the order and the first and second hitters would have traditionally been hitters who could run, get on base a lot, and perhaps get themselves or others into scoring position through steals, bunts and hit and run plays. Modern analytics has changed this a bit, but not as much as some suggest.
With the rise of analytics, it became clear that getting your best hitters up as often as possible in each game is important to overall run production and hitting the best hitters at the top of the lineup allows this to happen. But as you state, the leadoff hitter is guaranteed to come up with no one on base in the first inning, so it would seem like a bad idea for a team to hit its best power guy leadoff, even if he is also the best on base guy. Therefore, many teams now bat their best overall hitter second, which is why Aaron Judge has been the most likely 2nd hitter in the Yankees lineup in recent years. (Mike Trout has often batted second throughout his career as well.)
It is true that Aaron Boone has recently been batting Judge first on occasion, but he almost always bats Judge second and often places Anthony Rizzo third when Giancarlo Stanton is in the lineup hitting fourth, so he can put a lefty hitter between the two gargantuan righty sluggers. Neither traditional lineup construction nor the more modern, more analytically driven approach would suggest that batting Judge leadoff is a great idea in terms of average run production. However, quite a few analytical studies have suggested that lineup construction is overrated and not as important as many believe. So long as a lineup is constructed to get the best hitters near the top, it will likely be fine. The difference between batting your best hitter 2nd vs. hitting him 3rd or 4th is quite small.
Although I haven't seen the numbers, batting a slugger who also gets on base a lot like Judge first might actually increase your chances of scoring in the first inning, even if it reduces the expected average runs scored in that inning and later, since he will be batting immediately after the bottom of the order all game. With the Yankees pitching this year, the Yankees jumping out to any lead early can be deflating to the opposition. That might not be a great reason to try it occasionally, but it could be a reason.
Although it isn’t squarely on topic, the one thing I would add to all this is that the old school approach of batting a guy, who could run and handle the bat but wasn't great at getting on base, second has been a bad idea for a long time but is especially silly in today’s power focused era. (It might have made more sense in the dead ball era.) However, batting guys who get on base, can run, and can handle the bat first and second in a more traditional lineup can still work just fine.
The champion Yankees teams of the late 1970s led off Mickey Rivers, a speedster and solid hitter and on base guy, and batted Willie Randolph second. Randolph could run, handle the bat, and hit decently, but the reason batting him second really made sense is he walked all the time. His on base percentage was always very high, giving the better and/or more powerful hitters behind him (Thurman Munson, Reggie Jackson, Chris Chambliss, Graig Nettles) ample opportunities to drive in runs. If Isiah Kiner-Falefa were an on-base machine like Willie Randolph was, today's Yankees could probably do just fine with IKF hitting first or second, and Judge, Rizzo, Stanton, Torres and Donaldson following behind. But IKF isn’t and that isn’t this Yankees team. This team simply doesn’t have an obvious leadoff hitter in either a traditional or more analytically driven line up and it has no Willie Randolph. There is no speedster like Rivers or super high average guy who lacks significant power a la Wade Boggs. Most of the guys who get on base a lot also have power and the most frequent lead off hitter, D.J. LeMahieu, is a high contact guy whose ability to put the ball in play could arguably be useful further down the lineup where he would more frequently have opportunities to hit with runners in scoring position. (Aaron Boone has mentioned this himself.)
I know I have gone far afield, but in a nutshell, my response to your very sensible query is this. The decision to bat Aaron Judge leadoff on occasion is a bit odd and I would probably hit him second as Boone does most of the time, but it probably doesn’t matter much. Get your best hitters near the top of the line up and things should work out. Hope this overlong response was helpful.

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