Honestly, we will never have another good AVP game.
If you look at the trend of A/P games they are all releasing with less and less content. It would be a nightmare for a studio to not only make 3 different campaigns but a Multiplayer that will last and be balanced and fun.
Just comparing the Multiplayer of the games in the last two decades. We see that each one has less and less content.
AVP2
10ish maps on release (i forgot the total now there are like 600 community-made ones).
DM, TDM, Hunt, Survivor, Overrun & Evac modes. (Plus Lifecycle)
Each race had 4 different classes
Predator and Humans had 9 weapons.
AVP2010
I forget maybe like 6 maps on release?
DM, Mixed TDM, TDM, Infestation (Survivor MvA), Hunt (PvM)
No classes
Marines and Predator had like 6 weapons each
Aliens Colonial Marines (this one was actually fun, but the overall game ruined it)
9 maps
TDM, Extinction, Survivor, Escape
3 different alien classes
Many different attacks for aliens, and like 6 customizable weapons for marines.
No Predator (duh)
Predator Hunting Grounds
3 Maps
1 Game mode (about 8 different missions per map)
3 different predator classes, 4 (5?) FT classes
8ish weapons for Predator, a lot of marine weapons
No Alien.
You see a clear pattern of fewer maps, fewer game modes. Imagine if a game studio needed, to make 3 full-length single-player campaigns, 10+ multiplayer maps, 4+ different game modes, 3 different species with at least 4 different classes, and 8+ weapons to choose from. And things like Queen, or kill streaks and alien lifecycle. You need to do just that to match the quantity that AVP2 put out.
Taking game modes for example it probably took 1 experienced programmer a day to set up the different multiplayer game modes in AVP2. For Predator Hunting Grounds you would need to get voice actors, animators to set up a cut scene, and new art for the different UI elements. You would probably create an entirely new map exclusive to that game mode. That is extremely expensive and all triple-A studios are going to cut the fat and keep the polish.
The only way I could see an AVP game working is if an indie developer somehow got the rights and made a dedicated multiplayer game. And they didn't spend money on cutscenes, fancy animations, or customization/collectibles. Just pure gameplay focus. It will never happen of course because all publishers would shutdown that project since it has none of the 'sellable' qualities of triple-A games. That is exactly what happened to Predator Hunting Grounds, an Indie dev that had to meet triple-A expectations.