What about a new gamemode that includes the Warden and the players avoiding him?
It could be a “Hide from the Warden” type of gamemode, in which the players just hide from the warden in a closed area. (Like MM maps, but smaller)
Or rather a “Runaway” gamemode in which the players just run away from the Warden in a race, the last player standing wins kind of thing. It could include gadgets and artifcacts to annoy your opponents or the Warden itself.
Welcome to the forums @ShadowGaming972 hope you enjoy it here in the forums! 
Although it is a combination of h&s, MM, and DR its still a game tho
If this gets added, here are the things i need to know:
Happy Hiving!
Hey Sam
You don’t need to ping them every single time you mention them
Welcome to the forums @ShadowGaming972
However your suggestion may not fit in. As SamPlayzMC9029 has mentiones above:
There is one thing overall that may be a downside. Since this is a free-roam game. The games may be very slow but could be adjustable by player counts. But what i’m trying to say is, the warden is a very powerful creature and not even all top minecraft players even have a slight chance of defeating it.
However while reading through your suggestion I did get a game concept involving parts of your suggestion but its a mix and match I guess
I got an idea of a “Flee the facility” type gamemode. There will be objectives scattered across the map and you need to complete a minimum of 5 to unlock the exit.
But this is the hive we are talking about.
IF the beast is the warden, the player would permanently be blinded (as the warden cant see) but to combat this, there will be hidden sound sensors across the map that will alert the warden (player) to the location. If a player makes a sound and the warden is very close, their blindness gets removed and they will be able to hunt down the noise maker a lot easier
From when you said The players just run away from the Warden in a race, the warden only targets a singular entity that makes a sound. This game would be just a luck-based race minigame as the warden will target a random sound maker and they will be instantly eliminated. But for the other players, they can easily get away and just run to the finish.
IF there was parkour involved on the race, the warden cannot do the parkour as its AI cannot do that. Unless there is a way to make the warden larger and destroy the map as it walks forward would make the game more likely to be played. But still there are people bad at parkour and people good at parkour
This is just my opinion though
Fixing my Warden Gamemode Idea! (Part 1 maybe)
In the following link you can find a suggestion i made for a Warden Gamemode:
New Warden related gamemode idea!)
Though, i didn’t make things very clear, and there was some confusion around the idea. So i’m going to try resolving these doubts in this post.
In case #1, the “Hide from the Warden” minigame, the players do not need to defeat the big guy to win, when the game starts they have a 10 second countdown before he appears.
The objective around this game is just avoiding the warden, it could maybe have various rounds if there’s still more than 1 player alive when the time limit reaches 0. Or maybe the “room” or “area” itself could just become smaller as time passes, to make sure just one player remains and wins. Around the map, there could also be some snowballs or eggs to redirect the warden to a player’s location or just, getting him a little further away.
In case 2#, the “Escape from the Warden” minigame, the obstacle/parkour race i was talking about, could be a finite parkour race with a goal with the warden chasing the players from the floor under. The players will encounter artifacts to boost themselves throughout the race or to annoy players, (not hurting them).
Or maybe if you guys dont like the parkour idea, case 2# could just be a wide and enclosed map with no obstacles, just space and some circuits and pillars to make it a likeable map. As time passes, the map could become smaller to make sure just one player is left alive. (Example; “In 10 seconds, zone 1 is closing” and then whoever remains in zone 1 just loses and dies and so on) It would be a “Last player standing” kind of game, except the only capable of killing is the Warden, and everyone gets to run around the map and have fun.
The map itself could contain speed boosts or speed platforms to make the map more fun, and of course, the before mentionted artifacts. (Examples; Slowness Throwable, Speed Item, Invisibility item, 1 Hit Protection, Random teleports, Position exchange throwables, you name it.)
In case 1#, the map could be from 25x25 to 35x35 blocks wide. If small, may contain a second floor. In case 2#, the map could be from 30x30 to 45x45 blocks wide, with various walls and/or pillars all around it, like a labirinth with no exit.
And yes, in both cases the game would be luck based since the Warden attacks at a random noisy entity, but that’s part of the fun, isn’t it?
I hope i have resolved the remaining doubts about my idea, and i’d be open to answer any other questions moving forward. Have a nice day everyone.