IMO, Fighter doesn't need much incentive to go to 20, given that it has a very competitive level 20 feature. You can, of course, opt out of Battlemaster Fighter at level 12, but you're giving up a fair amount to do so. A second and third use of indomitable, a BONUS ability score increase (at level 14), a second use of action surge, your third extra attack, relentless, two maneuvers, one extra superiority die, and a die increase for ALL superiority dice.
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.
[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 and have removed your armor/shield is indeed a thing--and when I play, my PCs worry about and plan for the same scenario happening to them. If you're ready for
that you'll never be discombobulated by a mere Intellect Devourer attack, let alone a standard 5E "Medium encounter." Plans are useless but planning is invaluable.
Plus, an awareness that your friends could be dead tomorrow reminds you to treat them nicely today and enhances the strength of (fictional) relationships. There's no protagonist plot armor.