With the amount of advanced destroyers, I think it would be more important to increase ASW and air wing capabilities instead of pushing more VLS and anti-ship missiles.
That's not quite the way it should work... All types of ships should seek to have capabilities which are competitive with the threats they will face.
For a frigate, that means maintaining a degree of competitiveness in anti surface warfare and anti air warfare (newer AShMs, SAMs, VLS) in a contested environment, and also anti submarine warfare (ASW helicopters, sonar suite, UUVs, ASW missiles like VLA).
The nature of ASW is quite different to AAW or ASuW, because in the latter two, the number of missiles matter significantly, and in AAW radar and other active sensors are also important (often expensive and heavy). So for good AAW and ASuW, the size of a ship is actually quite important. A smaller corvette simply cannot perform the AAW of a cruiser due to lack of space for sufficient SAMs or a large enough radar and combat management system, nor can it carry as many AShMs to attain the same ASuW capability of a cruiser.
But for ASW on most typical surface combatants, it's very much all about the ship's own sonar suite, and especially the capability of the one or two ASW helicopters they carry. A shipboard sonar suite can very much be effective in ASW without being massively large (for instance, many VDS and TAS can be fitted onto corvette or even FAC sized ships), and ASW helicopters are limited by size and the quality of their own sensors, datalinks, and onboard weapons.
Smaller surface ships may actually be better in ASW because one would be more willing to risk a smaller corvette or frigate playing tag with potentially small, old and low cost submarines (which are still potentially deadly, quiet and elusive) compared to a destroyer or cruiser.
So what I'm saying is that depending on a ship's mission (multirole frigate in this case), one can and should very much increase a ship's AAW and ASW capabilities to remain competitive, while also seeking competitive ASW capabilities.
The only way to increase ASW while "not pushing" other realms like AAW, ASuW, would be to cut out those capabilities almost entirely (such as not including VLS, not including any advanced radar, reducing AShM number), and use the increase in space and free displacement to redesign one's ship to maybe carry more or larger helicopters and larger sonar... however I think that would be a poor decision to make, and even the best surface ships ASW platforms today retain decent AAW and ASuW capabilities