I understand the argument that Battlefield is objective-based and that win/loss ratio should matter, but I don't think that makes K/D unimportant. In fact, K/D is one of the most useful measurements for identifying large differences in individual combat skill.
If I'm roughly a 1.0 K/D player and I'm repeatedly fighting players with 3.0, 4.0, or higher K/D ratios, those players are demonstrably killing opponents several times more efficiently than I am. Regardless of whether Battlefield is primarily about objectives, I still have to physically fight those players in order to capture or defend those objectives. If the skill difference becomes extreme enough, the objective game itself becomes harder to participate in because I'm spending significantly more time dying and respawning.
Win/loss ratio also has a major weakness as an individual skill measurement: Battlefield is a large-team game. I can play extremely well and still lose because of what dozens of other players on my team do. Likewise, someone can have a high win rate without personally being an exceptionally strong player. K/D isn't perfect either, because someone can protect their K/D while ignoring objectives, but it measures something that win/loss doesn't measure very well: how dangerous that individual player actually is when you encounter them.
I wouldn't suggest matchmaking exclusively by K/D. The game should look at several things—K/D, win/loss, objective score, score per minute, recent performance, and possibly other statistics. But K/D should have meaningful weight when the system is determining individual skill.
And I don't think this requires extremely strict skill-based matchmaking. Nobody is saying a 4.0 K/D player can never share a lobby with a 1.0 K/D player. The goal should simply be to prevent the extremes from happening constantly.
For example, if the player population allows it, someone around a 1.0 K/D should generally encounter people somewhere reasonably around their ability instead of routinely being used as fodder for 3.0–4.0 K/D players. And if those very strong players have to be in the same lobby because the population is small, then distribute them between the teams as evenly as possible.
That actually addresses the declining-player-count argument rather than conflicting with it. You don't have to make matchmaking so restrictive that queues take forever. You can loosen the acceptable skill range when necessary to fill the server, while still having the system prioritize the closest reasonable matches first and balance the teams afterward.
The point isn't to guarantee everybody a 50% win rate or protect players from ever facing someone better than them. You should face better players—that's part of getting better at the game. The problem is when the difference becomes so enormous and so frequent that an average player barely gets an opportunity to compete.
There's a huge difference between fighting someone who is somewhat better than you and repeatedly being fed to somebody operating at three or four times your combat efficiency.
Good matchmaking doesn't need to eliminate skill differences. It just needs to keep those differences reasonable enough that both sides still get to actually play Battlefield.