If you have tier-1 soldier group consist of 10 men you were getting 30xp in old calculation. Now you get 2xp per soldier means that in total you get 20xp for your tier-1 group. So xp gains did not changed much for tier-1 groups. If you have 20 men in one group you get 40xp for that group which is more than previous implementation. Any one perk does not supposed to train your troops by itself only. We have hundreds of perks and any of them cannot be so powerfull. You will also go into battles time to time if you have this perk probably about 15% xp gains will applied by this perk to your 1-2-3 tier soldiers and 85% will gained by battles. We cannot make effect of one perk equal to battle rewards.
These perks are only side effect. We will add more. If you collect several of them you can upgrade your soldiers easily without battles.
You guys are obviously experienced game developers if you can create a game this complex. Then why does it seem like you forgot the basics of game design? The player needs to at least FEEL he's making meaningful choices as he progresses through the game. If the perks are 'only side effect', you may as well remove them completely, it would save much frustration to many players (btw, having most of them not working at all at the moment is unjustifiable, especially since there are already mods out there that make them work). Character leveling and acquiring new skills/attributes/traits is one of the core components of making the player feel he's accomplishing something as he plays. I like your character development system in almost all respects. Don't trivialize it, it makes no sense and has no good outcome if you do that.
Also, it's true there are hundreds of perks IN THE GAME, but you forgot that due to exponential ramping up of difficulty in achieving higher levels, one character cannot acquire even close to all of them at once. We already need to make choices as to which skills we will focus on (which is good, see above), but then our choices need to feel justified when we reach higher levels of those skills. Otherwise, the whole system becomes almost pointless.
As for these two concrete perks, when you get to the middle/late stage of the game where there is constant battling, you inevitably often lose part of your troops. To then be forced to stop the warring and go recruit new troops, then hunt down looters for a period of time in order to level up your new recruits is just a chore and unwelcome distraction at this point of the playthrough. Going from facing armies of trained soldiers to fighting looters again is going backwards. An alternative of training your recruits in 'real' army battles is not an (good) option, for various reasons. So maybe buff the effects of these perks, but move them further along the progression to coincide better with this stage of the game?
Lastly, a suggestion: take a look at the most popular mods and take notes of what players are most bothered by in your design, then act accordingly. Remember, you are not creating an art piece, but a consumable product. As many people as possible need to enjoy consuming your product.