So, no AT802/OA-1Ks with the F-16 radar in a pod?
It's a two-way problem.
1 part is police action, taking into account explosive growth of civilian UAV usage. Those can keep rotorcraft speeds, but they will probably need hover as a prerequisite. Helicopters probably do that.
2 part is military intercept. And here problem is one continuous threat profile from 100 to 1100 km/h, from 5 to 5000m. It should be something with extremely capable sensor field, capable of flying slow and fast, safely and precisely.
Then big intercept.
Skipping smaller types(fighter-interceptor, etc), we broadly speak about 3 tasks.
-Defca. Should be done with an air superiority fighter, but either fighter or entire system should be focused on being able to target and entangle LO threat, including one flying at low altitudes. Basic assumption is that this threat not just fights back, but actively seeks to destroy defca fighters and win air superiority.
Broadly, it's su-57 personified. But there's a question how you do it on the next tech turn.
-LACM intercept. LACM intercept is catching many individual LO or VLO targets, which also get AI and are likely to learn to defend themselves.
This task always require largest possible pool of MRAAMs (and ideally IIR-APKWS type as a backup) and powerful search/targeting sensor, but geographic spread determines optimal carrier.
Broadly, best available modern LACM interceptor is likely F-15EX, but many fighters can do it in principle.
-Loitering interceptor(BARCAP is a subtype), probably against modern bomber threat. A major problem, requiring ability to rapidly scan wast space(speed, powerful sensors) against broadband VLO targets, which can't be effectively found/targeted via radar (and which also can and will fight back).
Some respite can be found in that modern generation of VLO bombers likely can't really go down, i.e. large aperture optics(J-36) are likely the way.
But J-36 in my opinion is a subsonic cruiser, which can go supersonic if really necessary. Here you'd need a supercruiser, operating with multiple loyal wingmen.