In a way, a really slimmed down Eternal would be a really good arcade game if those things still existed.
That's Doom 2016. Eternal made the arenas way more arcade, but in terms of gameplay itself 2016 does straddle that line between old-school and arena shooter. Because the Arenas in 2016 usually have multiple paths you can take to circle around them, you not only hold but also pick up a lot more ammo just by going around, and while some enemies are
easier to kill with some weapons it's not a mandatory thing like in Eternal.
How both games treat the chainsaw is indicative of just how overdesigned Eternal is. In Doom 2016, the Chainsaw is a special weapon with very limited ammo that you use in two specific situations: 1 - you want a specific enemy dead
right the fuck now, or 2 - you fucked up and ran out of ammo (either in general or for your favorite weapon). So unless you were playing on the highest difficulty you would only use it once every few encounters. Most of your ammo would be picked up from enemies you shot to death, or from pre-placed pickups around the map. In Eternal, the chainsaw regenerates ammo insanely quickly and it's meant to be used not only every fight, but often
multiple times per fight because the game keeps throwing waves and waves of demons at you, and your ammunition supply is so fucking limited. The chainsaw in Eternal is supposed to be used so often that pretty much every arena has infinitely respawning melee zombies for you to use as ammo/health pinatas. You'll notice that maps in Eternal have a lot less pre-placed ammo boxes lying around because of it. The zombies are your ammo dispensers.
Doom 2016 railroaded you into arena fights, but once the doors were locked you got to make your own fun. Want to kill the entire swarm of zombies with the Super Shotgun? Have fun! Chaingun everything to death with infinite bullets? Knock yourself out! Rocket Launcher with guided rockets? Sure! Pistol only? Good luck! Eternal on the other hand is a classic example of an overdesigned game. There's only
one way to play the game, and the developers won't have you playing it any other way. And it shows, too! You could see the devs were angry when people found ways to cheese the Marauder by stunlocking him with the ballista, for example.