Such a supersized interceptor would only work if your opponent does not have BVR, or else it is going to struggle to dodge incoming missiles. The Mig25 and 31 got away with terrible agility by being very fast and can usually outrun any missiles shot at them at BVR and sometimes even WVR ranges. A modified B1 would not have that even with F119s.
So it cannot outturn or outrun incoming missiles and would be reliant pretty much completely on soft kill measures to survive. Just not very practical.
s.
Actually, It CAN. The concept of B-1R is based on the fact the B-1R has enough fuel capacity for a very long radius of action in addition to being able fight an entire engagement, from initial contact to final exist, at full afterburner and Mach 2.3.
With fully modulating air intake and f-119, B-1R would be only fractionally slower than the mig-31, but it can stay in afterburner and remain at its top speed far longer than a mig-31 can and thus in reality cover more distance during the time a very long range AAM chasing it can stay in the air, than a MIg-31 can. Starting from a BVR position at 40,000 feet, 40 miles away, and 60 degrees off nose towards the enemy fighter, a B-1R already at mach 2.3 and able to sustain that speed for 5 minutes will be able to fire its own missiles, turn and out run any known AAM launched from any altitude.
Given B-1R's higher entry speed, it's own AAMs will have signifanctly greater range, as well as higher end-game enrgey state for the same engagement, than if the same missile is launched from most normal fighter, including the F-22. So the very same AAM fired by a B-1R will be more effective and harder to evade than if it were fired from most other fighters. Most fighters can't turn to out run or evade an aim-120C fired by the B-1R during the scenario stipulated above.
Given it's large payload, B-R can saturate the battle space with its own missiles as well as counter measures and greatly add to situational awareness difficulties of the enemy.
So it's an unorthodox, but far from flimsy, concept. It does depend on BVR missiles being as effective as advertised for the B-1R to be able to shoot anything down. But unless BVR kinematic performance are far more better than advertised, it is safe from being shot down.