Fanaelialae
Legend
I can see that with Eldritch Knight and even champion, because Champion's Survivor really is awesome and Eldritch Knight gets spell progression in the levels between 12 and 20 (2nd level spells => 4th level spells). But the Battlemaster...
If you go Battlemaster 12/Arcane Trickster 8, you generally increase your damage, against any foe with a high AC where an ally is adjacent or advantage applies. E.g. vs AC 19 Adult Red Dragon your DPR goes from 34 to 38. Yes, you miss out on an extra action surge and two Indomitable usages, and you have 5 d10s for seven maneuvers instead of 6 d12s for nine maneuvers, no Relentless, and one less feat. In return you gain Cunning Action (which could boost DPR even further via Hide against tough foes, and also helps mobility), a suite of defensive spells (Shield, Invisibility, Blur, Mirror Image), Evasion, Uncanny Dodge, and Expertise on your Athletics/Stealth/Perception checks (plus one more). Evasion alone probably makes up for the missing Indomitables, especially since you've already got one and there are diminishing returns.
Maybe it's because of playstyle, and the fact that I prioritize survivability[1], but the Arcane Trickster additions look way better to me than the battlemaster's mild increase in spike damage output and extra feat.
I never said that multiclassing Arcane Trickster was a bad way to go, but I don't see it as being strictly superior to Battlemaster 20. It's arguably better in terms of survivability, but you're giving up a significant amount of nova ability in order to do so.
Fully leveled, the Fighter/Arcane Trickster can make two attacks with a +4d6 sneak attack each round, using Action Surge once to make four attacks (only one of which can be a sneak attack). Using action surge he can make six attacks over two rounds with 8d6 bonus damage from sneak attack. Additionally, he cannot use GWF if he wants to also use sneak attack (which may or may not be relevant depending on whether GWF is even allowed).
The Battlemaster can make four attacks, and use Action surge twice to make four additional attacks. Using action surge he can make sixteen attacks over two rounds. There are many cases, where I'd rather have Indomitable over Evasion (anything that doesn't involve a Dex save). Evasion isn't that amazing since all it does is reduce damage. As a fighter I'd be more concerned about things like Hold Person or Mind Blast, which is where Indomitable will be of greatest benefit.
I'll grant you that the Arcane Trickster is probably generally better from a defensive perspective. However, defense is not the be-all, end-all. Sometimes you just want a character that can crack some skulls, and leave defense to someone else (or else run with the "a good defense is a good offense" strategy and hope for the best).
[1] E.g. due to the dynamic-sandbox nature of my world, surviving an ambush by ten Mage Armored Invisible Stalkers when you're bedding down for the night is indeed a thing--and when I play, my PCs worry about the same scenario happening to them the same thing.
I would never leave home without Leomund's Tiny Hut or Mordenkainen's Magnificent Mansion.
