Probably easier to take an Oresund service from the Airport to Malmo and connect there rather than going back to Copenhagen.
Indeed so - and they're more frequent from Malmo C as well.
Note that the passport control is only the half of it - the peak frequency on the route has halved, leading to some very crowded trains.
What you used to have was a seamlessly integrated system from Helsingor and Copenhagen through the airport, across the bridge to Malmo, and on to other destinations in Skane (plus Gothenburg). Actually, inter-city traffic is relatively low - the big loads come from commuters around Malmo and Lund working in Copenhagen.
But then these regulations came in and... Ouch. The airport station (two platforms on two tracks) was split down the middle with fences going up. All eastbound trains now terminate here, and you had to shuffle up the travelators, then queue to show your ID to contractors (who weren't fully versed in visa regulations - lots of people with less simple immigration statuses got incorrectly turned away) before shuffling back down to the now Sweden-only platform, on to an overcrowded train running every 20 minutes (rather than 10) towards Malmo. With long queues, you may miss the connection and have to wait another 20 minutes.
On arrival at Hyllie (the first station in Sweden), it was initially an utter mess. Temporary crowd fencing had been put up on platforms with trains coming from Copenhagen, so those exiting in Hyllie had to go through Swedish police checks (and those on the train had to have the same, while the train waited for the police to give the all-clear). There were frequent, unpredictable delays. It was never entirely clear what you had to do if you wanted to take this train domestically, so a lot of people went for the Pagatag local trains, then changing in Malmo. It messed up a lot of domestic transport in Sweden, too. In the meantime, things backed up with the slightest delay on the Danish side (as there was now only one platform available for Danish trains). To add to the complexity, trains heading westbound went straight through, but to avoid congestion, they'd skip the airport if things got busy, not helpful if you're going for a morning flight.
Thankfully, the police at Hyllie have taken a back seat. Rather than adding up to an hour to your commute home, it's more like 20 minutes (unless things are busy at Kastrup).
Reductions in numbers are likely due to a number of factors: people changing jobs, people carpooling over the bridge (the tolls are 50 each way for a one-off ticket, but this comes down to 10-22 each way for frequent users - still not insignificant). Buses still attract police searches. Some commuters have bought boats, others from further north have returned to the H-H ferry.
It's not pretty.