I'm not converting anything literally really. Just gauging his impact.
The D&D Tier system in 4e and 5e are based on what effect you have and how much an impact you have on an area.
Hawkeye has a lot of power but ultimately he doesn't and hasn't be shown to to be a threat of anything above the regional level. An average lord or lady of a D&D duchy might not have knights able to take down Hawkeye but the king or queen of a national would. Because Hawkeye has not be shown to be able to take on a national level threat.
This is why most fans' perceptions are off.
As an example for your point and general fighter capabilities I’d like to propose kung-fu panda’s Tai Lung?
I know he’s a monk yadda yadda all that but he’s still an incredible example of what i think a high tier martial should be capable of, He doesn’t have any magic powers or anything it’s all just pure skill and physical ability, as a fighter i think that all would change is his movement bonuses would instead be defensive armour and the fight would move around less as a result but would go on for longer, plus he’d be using weapons more than unarmed strikes.
If your prescence doesn't invoke "We must inform the King/Queen that X is here." because of the power of your features, you are not over level 10.
“Tai Lung has escaped, He is coming,
We must evacuate the valley.”
There’s no king or queen involved but I feel this carries the same weight to it.
A list of examples of good ‘fighter’ things I think are shown throughout the movie:
-Ripping off a (quite chunky) metal manacle with a single bare hand
-Him throwing(kicking) those massive ballista bolt like they’re hand spears
-Disarming an opponent, taking their weapon and attacking them with it
-Ploughing through the rhino guards with ease, tossing them all over the place like they weigh nothing and even throws/knocks around one or two to attack others
-He simultaneously takes on four of the furious five(Mantis is stuck holding up the bridge they’re fighting on) who are all but not quite as high level fighters(monks) as him and holds his own for most of it, they don’t even defeat him they just have to resort to tying him up in ropes(which he promptly breaks out of again)
-Shattering the stone floor to pieces with a single strike(that’s a 5ft AoE attack at minimum, 10ft if you’re being generous,
maybe 15ft if it’s only to trip opponents)(was a kick in movie but just as possible with a weapon strike)
-And then easily proceeds to throw a small car sized boulder from that broken ground
-Swings and launches an entire display rack’s worth of weapons in a single action
-Fighting an opponent while in a sustained grapple(falling down the stairs while he and po both grip the dragon scroll)
-Causes an entire (solid stone?) building to collapse with a single blow
There’s probably more if I rewatched the entire movie but you get the idea, martials don’t need to suck just because they’re not using magic.
Have some movie clips of the points I described. (I hope these embed properly)