I think the reason behind the switch is
More seriously I think because it's more in line with their nearby allies like the French and Spanish who similarly have more frigates. One provides an ASW Frigate the other a Air Defence Frigate and you have a navy (joking) none have huge fleets so they combine forces in task forces for the UN or NATO
And because looking at the armaments of their ships German frigates seem to specialise in one area or another so air defence or ASW instead of both like the American Arleigh Burke.
As their smaller and more specialised they are frigates
Most of those units can be adequately described as multi-role. They can perform in all three of the physical domains of warfare, but not at once. Believe it or not, it's actually impossible to undertake ASW with any other type of physical warfare, it just doesn't work. Mind you, traditionally speaking I'd say that surface based ASW just doesn't work, except as a novel method of assisted suicide.
You'll find that most modern navies run Frigates for two real reasons. One, they're primarily multi-role, two, cost. The lack of an internationally recognised ship type convention notwithstanding, Frigates all tend to be around 3000 to 7000 tons, lighter, smaller and less complement. While a Destroyer or Cruiser would be a superior combatant in blue water combat, they cost a lot more and aren't as effective in littoral combat or constabulary roles. The Oliver Hazard Perry class Frigates embodied the concept of multi-role, even as aging combat platforms they provided effective service in counter piracy and smuggling, having excellent endurance and enough crew to perform the role.
