We are probably going to get a “working as intended” here, but lets take a look at it.
Stats don’t actually confer any specific team score bonus. The things that give stats globally usually coincide with some kind of bonus based on what stats they added, and in the major team score revision (the one that thoroughly broke PvP points for a while) nearly everything that gave a global skill point also gave a global score bonus, and the all gave differing amounts of bonus based on the skill bonus conferred. But this rule has never applied to stats gained from stuff like team bonuses, pet boosts for team bonuses, or weekly bonuses. I believe medal stats are not implemented as fixed global stats, but rather a “team stat bonus for every single team”.
Aside from implementation issues, I believe that the reason this is unlikely to change is because you can remove and equip badges whenever. 24 life or armor or 12 magic, if using the kingdom scale, would be worth 960 score points. Anyone who has done the “leave your guild and play PvP” experiment knows how much this drastically alters payouts, and that is a score differential of 1480. With endgame stats in every other category and a personal score of 13500+ fighting teams with scores of 13000-14000, equipping them would drastically lower your payout. It would only be if the defense team had the stat medals equipped to see 14000-15000 teams and the matchmaking correctly served them to you that you wouldn’t see some kind of gold loss, and we can’t count on either of those. At the same time, if it did work like that, removing equipped badges could see my three trophy battle gold payout rise by as much as 80% (although, honestly, it should be there anyways semi-normalized for end game, just like PvP points are). And then what of cedrics? They clearly have the most impact on any given PvP match, but how many “points” do we assign to those? Even if they were factored into matchmaking, what happens when you pull something based on that matchmaking, then they change their medals, tanking your potential payout?
Now, elite levels, if those aren’t giving some kind of score bonus to the team they are on… they 100% definitely should. Not based on the stats gained, again, but a flat score applied to each elite level, more for each successive elite level, like traits.