There are two parts to the equation... engine size and air-mass requirement.
The first required a minor modification in the lower aft fuselage of the UK's Spey-engined Phantoms, but the second required the entire intake and ducting to be enlarged in cross-section, which increased drag - reducing max speed and eating up part of the fuel economy savings in going from the J79 to the Spey.
J79: 31.6" body diameter, 39.1" afterburner diameter; 170 lb/sec airflow; SFC* .85/1.97
PW1120: 33" body diameter, 40.2" afterburner diameter; 178 lb/sec airflow; SFC .80/1.86
Spey RB168: 37.5" body diameter, 44" afterburner diameter; 210 lb/sec airflow; SFC .63/1.95
F100: 40" body diameter, 46.5" afterburner diameter; 225 lb/sec airflow; SFC .76/1.94
As you can see, the F101 would require much greater modifications in the intakes and ducting, which would increase drag etc much more.
* SFC = specific fuel consumption, given in lbs fuel used per lb thrust per hour