I think one contributor to the general lack of combo cooperation is how easy it is to miss the window of opportunity on them. Nostalgia may be tinting my perspective, but in ME3MP I remembered the combo primers lasting for quite a while - upwards of 8 or 10 seconds on a lot of them. They also had immediate visual feedback - biotic primers made their victims glow bright blue, fire primers set their victims on fire, etc. If you had eyes on target and it got hit with a combo primer, it was immediately evident - and the effects lasted long enough that if you had a detonator on cooldown, it would still be there by the time it refreshed.
Now contrast the combo primers in DAMP:
We have four primers, all of which incapacitate the target - Freeze, Stun, Sleep, and Paralyze. Of these, three of them typically have short durations - 4 seconds or less, as low as 2 seconds in the case of a paralyze from Static Cage. The other, Sleep, breaks when the target takes damage. This means you have a far shorter window of opportunity to take advantage of a combo primer. Now, this was never an issue for me in single player, where I could immediately pause after using a primer, take however long I wanted to select a character with a detonator, and queue up the pain, but in multiplayer where you not only cannot pause, but you're also at the mercy of latency and connection quality (with a distinct lack of dedicated servers, *ahem*), and this becomes a recipe for whiffed combos.
Also consider the visual feedback of the primers in DAMP: Freeze is probably the most visually distinctive and obvious, what with turning the victim white and shiny, but... that's about it. With Stun, Sleep, and Paralyze, the victims just sorta stand there. All the DAMP fights have a lot of visual clutter - player abilities, creature abilities, environmental effects, etc. In terms of visual design, these combo primers plummet right to the bottom of what attracts your attention. Yes, there are little scrawling text messages, but there's already tons of floating scrawly text in the middle of a fight, and it's not a good indication of how long an effect persists. What I would have personally done is make it so that while a combo primer is active on a target, put some kind of obvious glowy icon above their heads - like, a snowflake for Freeze, or the little orbiting stars for Stuns. Make them big and immediate, and make them last for as long as the effect persists, as a sort of "Use a Detonator on this guy!" sign.
Oh, another contributing factor I've noticed is that because the combo primers are tied to incapacitating effects, you end up with this non-intuitive mix of enemy types that are just immune to certain combos because of their immunity to that associated incapacitator. You do end up with a sense of what's immune/vulnerable to what after playing for a while, and you can check on enemy units while you're in the fade, but that information is very... obtuse for new players (and/or the less observant ones). This also results in a kind of strange (to my mind) set of interactions where the weakest grunts, by virtue of their vulnerability to the broadest spectrum of primers, are the ones that get hit with combos the most often (resulting in a kind of hilarious overkill), while the big targets, whom you'd think would be the prime combo targets, are immune to a bunch of things and hence people don't bother trying to set up combos on them.
With all that said, I do enjoy the combo system in the game. I think it adds an entertaining aspect of teamwork, but... I'm almost always playing with an old friend on a solid connection and we're on voice chat, calling out targets to set up for combos a priori. When I'm playing in a PUG, especially one with a shoddy connection, heh. Good luck.