Not really the Mig-31 can fly faster than PAK-FA and can sustain those speeds for long and it also carries the longest range AAM
In return the Mig-31 can also be detected by a modern AESA and sensor fusion much further away than the PAKFA (regardless of whether it is emitting or not).
AAM's are limited by the network and the detection range for your FCR. You can have a 100nm AAM but if you cannot detect and effectivly target a PAKFA or F-22 from 100nm the range is useless.
so if GBR comes into the picture then Mig-31 can excute the long range interception of the target much better not to mention at M 2.8 the kinemetics afforded to AAM would be much much higher
The problem comes from the fact that the shrinking effect on GBR's that a VLO fleet provides. We are not talking about 1 f-22 or 1 pakfa..We are talking about a force of a few dozen, equipped with a few dozen bombers, UCAVs and what not with a barrage of LO Stand off cruise missiles from legacy aircrafts some 400-500nm away. The more the GBR envelopes are shrunk the more the interceptor has to rely on its own SA to carry the day. The PAKFA is much better here since it can fly silently using its LPD sensors and get close in for a kill. Even with the radar turned off the Mig-31 has a huge RCS that it will present to the attacking force.
I would suggest you read Yefim Gordon book on Mig-31 and why an Interceptor is good at certain role than a general purpose multirole fighter or an air superiority fighter
And I would suggest you try to analyze what effect an All stealth attacking fleet has on the modern intercept mission. The underlying assumptions that made the Mig-31 or other interceptors work earlier do not hold true given the change in dynamics. Either you develop a VLO interceptor (again arguable utility) or you develop a capable Air to Air fighter with a good supersonic range, Vast amounts of SA gathering ability, a good loiter time (TOS) and VLO design so that it can operate freely outside of enemy attack envelopes.
Similarly, a YF-12 upgraded with modern sensors is useless to fend off attacking PAKFA's , PAKDA's and future russian UCAV's. It will provide limited utility unless somehow it is wrapped in a VLO design (where flying fast is counter productive). TOS will trump speed for detecting and successfully fending off large attacking VLO fleets.
The PAK-FA can never be an interceptor reason why the Russians are working on a follow on interceptor although it wont be a dedicated interceptor we know it now in Mig-31 but more like for Aerospace Defence
When it comes out (if it does) it will look a lot different than the Mig-31. The mission itself has changed and therefore platforms must adapt.