I'd still rather see perks, trader pods, and dosh disappear entirely and move to a more RPG route with better weapon upgrades purchased at the start of every game with Vosh.
In this system, base stats and levels are attached to the characters. Donovan "Bulldog" Neal, being a boxer, would naturally have good HPs, strength (good for recoil reduction, melee damage, and carry capacity), speed, and stamina, making him a natural zerk to build upon. Without formal training, he'd be, overall, terrible with guns, armor, and science (such as healing, explosives, energy weapons, and welding).
Masterson might be great with assault rifles, explosives, and armor, but only average with hit points, carry capacity, and speed. He starts with some armor and thermal goggles, but the weight of those items slow him down and reduce his carry capacity until sold or depleted.
You get the idea.
Leveling up happens at the completion of every contract. If your character primarily used a shotgun during a game and her base shotgun stat is 10 out of a possible 100, then there is a 90% chance that she learned something new and will be 11 out of 100 starting the next game.
Meanwhile, your friend has played a lot more and has built a shotgun stat of 90, making her already very effective with them. She only has a 10% chance to improve, thus creating a non-linear learning curve. Your character starts with base stats but becomes as unique as you play her.
Want a well-rounded character? Use anything and everything at your disposal. Want a specialist? Get picky.
As your proficiencies improve to certain levels, you unlock skill options, similar to the perk skill options utilized in KF2. Your SMG stat is up to 20? Congrats! Choose one: reload faster, switch faster, reduce recoil, faster iron sights, etc. with SMGs. If you choose to specialize in SMGs, then you unlock higher tier SMGs and skill improvements with SMGs faster, but your learning curve with other weapons is slower.
A new Social stat can affect teammate morale. Donovan, for example, might impart a resistance bonus to nearby teammates, which is lost if he dies. The Social stat naturally goes up as you play with others, but goes up faster when you protect teammates, share resources, rack up assists, and heal others (and might be penalized if you shoot teammates). The Social stat can be upgraded with a larger morale radius or potency for both player and teammates.
"Leveling up" would revolve around learning things as you go, but if you want to change your character's base stats, they'll need to go through special training, which takes time and discipline...
...just kidding. It takes money.
When you've completed enough contracts and can afford it, Vosh can be spent to "send your character off for training." Mile High training can increase stamina. Weight training will increase strength, giving you the option to boost melee damage, recoil reduction, carry capacity or a little bit of all of them. Target practice will increase accuracy with guns. Etc. This would become the new Prestige characteristic, which unlocks more dangerous/lucrative contracts.
Vosh can also be spent to change your starting loadout, which include higher tier weapons (if your character is specialized enough) and items that you can give to teammates. Otherwise you might start with just your fists (or whatever defaults with your character), and you'll have to make scavenging a priority.
Players with high prestige levels might also find that they need vosh to re-buy their loadouts whenever their character dies. Having to spend your vosh on loadouts rather than training provides another form of non-linear progression.
While I'd love to see the Trader offer more options (hollow point/armor-piercing ammo; soft/steel/ceramic armor options; healing dart/grenade/vertical grip under-barrel attachments; various optics; larger ammo belts; etc.), including temporary player buffs via implants or equipment enhancements (eg, upgraded syringes that are more potent, faster charging, and/or buff different stats), I think an RPG system would make more sense for character upgrades, allow players to play how they want to play (eg, KF2's support role character limited to shotguns seems arbitrary), reduce the impact of "balance", and make it easier for team-building (eg, only one Ana Larive per team and limit teammates to certain prestige levels).
I also believe it would balance itself out by simply having to pay for it.
I trust that you didn't mean this in a pay-to-win sort of way