I don't know if this would be possible or worth implementing for the devs as it may only appeal to veteran players who have already enjoyed the game for a long time.
I'm confident that every player who has chosen to play on Dominating has played through the game multiple times before. Most have likely memorised oddity locations. A prevalent strategy after finishing Junkyard is to head to Foundry for easy levels. Apart from the hobos, no danger is involved. No skill point investments are required to access Evelyn's bunker through the slum entrance.
There are oddities scattered throughout Underrail that don't require significant effort to acquire like the human scalp, the rathound book, lanterns, mushroom booze bottles, zip lighters, barrel ladles, train tickets, and the core city plans. Players that invest points into either stealth or tailoring can easily acquire even more oddities. Creatures like the psi-morph worms drop 1XP oddities worth a total of 4XP but can be easily culled relative to the player's current level at Foundry.
On subsequent playthroughs of Underrail I've always opted to play Dominating on Classic mode. Oddity mode is the definitive way to play the game because it encourages and rewards exploration, these go hand in hand to create an awesome experience. I don't know if other players share my opinion, but that experience disappears after a few playthroughs of the game. When new players try Underrail they don't know if wading through the Burrower nest at GMS is worth it. The possibility of a great reward can be an exciting prospect but veteran players have already learned the hard way that it's not worth it. Randomised oddities may incentivise those players to attempt it again despite being aware of the effort required.
Spawning the oddities with a higher chance in uncontrolled zones and a lower chance in fully controlled ones might be an interesting way to spread them out. Even just shuffling them around would be fun. Imagine finding shadow dust on your shelves at SGS!
Corpse oddities may not need to be randomised as they are not in static locations, but adding static oddities onto corpses in addition to corpse oddities might be interesting (assuming it's not impossible, or worth the time to implement). Having a higher chance for an oddity to drop on more difficult enemies like Industrial Bots or the Black Crawler would also be fun.
This may be an interesting way to add even more challenge to Dominating.