Interesting as both cases had fire warnings. In the case of the BA 777, it was hardly a "high speed" reject, I believe they did not even reach 80kts.
The interesting thing about the fire warnings is that they did not occur at the time of the engine failure but some time afterwards. In the Manchester accident, it was ~10s later and they were deliberately not braking much because they had (incorrectly) diagnosed it as a tyre failure. At LAS, it was similar, with the fire warning only coming as they were slowing down with manual braking. By the time the warnings were received and understood, both of the aircraft in question were well alight.
Examples like that support the idea of bringing the aircraft to a halt ASAP, even if the reject happens at slow speed, because at that point you just don’t know how severe the failure actually is. The 737 took ~45s to come to a halt on a taxiway after aborting from 125kts, which didn’t help survivability. If in doubt, stop quickly on the runway.