Boons must have really impressed him.
Yup and none of that is anywhere to be seen in 5e not even in those boons that will suddenly make the guy from gym feel awesomely epic as he performs the same maneuvers he could at level 3 either.
4e presents for me a natural progression into legendary and mythic range and begins with a hero 5e really feels like a stall out.(maybe not for casters)
Unless I missed something the 5e fighter very likely has nothing at 20 that he couldn't have at level 5.
I'm not really a 5e guru, maybe some of the new books have some sort of options I'm not up to speed on, etc. Playing the battlemaster though I didn't run into any sort of capability which really changes materially from level 3 on. You get a few more of certain things, you get 'Indomitable' at level 9, but that's not really spectacular, it just gives you some extra saves. You get more/bigger superiority dice, and extra maneuver picks, but its all from the same list you choose from at level 3. You can obviously choose feats, but again its not like there's some higher level list of crazy ones that do something amazing.
Certainly a 20th level Battlemaster will be supernaturally resilient, and get a lot of super strong weapon attacks. He can get a lot of those attacks, and add more with Action Surge, and will get at least one superiority die per turn, guaranteed. He still cannot pull any trick he couldn't pull at level 3. Potentially he can make ability checks in some undefined situations which will pass 'impossible' grade checks, but when, where, how, and if those checks can be made is not really defined by the rules.
I see nothing at all 'epic' about this character. He can of course probably kill some very nasty looking monsters with his weapons, but that's it. I agree that the Epic Boons don't really excite me. Looking at them, they're honestly not even mostly on a par with high level spell slots. They seem more like basic thematic elements that I would more closely associate with something like 15th or 17th level or higher play, basically (what 5e terms the 'Masters of the Realm/World'. I would not consider them 'capstone' type abilities, and frankly non-casters in 5e simply lack such, entirely.
In contrast every 4e ED provides abilities more thematic of really high level play IMHO than any of these. Well, there are a few 'dud' EDs out there, but given that there are a couple hundred choices...