im not saying dont run. however, most experienced trainers, runners etc will tell you a critical factor in speed is strength and power.
the further you travel per natural stride, the longer you will be able to run, and the faster.
high weight low reps is the faster way to increase brute strength. running with a weight bag, with ankle weights etc will all increase strength, but a session of weight training can serve just as well, and is less likely to cause injury.
so many factors are involved in running performance. for most people they reach there limit when only one of these maxs out. ie your legs ache so bad, you just run out of energy etc.
if running is pretty much all you do, then this weaker area will be worked hard. your other areas do not get the same intesity level. if your legs give up, you stop, but your heart and CV system could keep going for longer, and only gets a smaller relative workout.
if you train seperate areas at a time, you can in theory get all your running factors near equal, so that your CV starts to have a hard time at about the same time as your legs start to turn to jelly. that way your training will be more efficient.
the phrase that is banded around a lot on here to do with PRMC:
"one good repition is better then 5 bad ones"
same goes for running training.
if you care to read:
http://www.coolrunning.com/engine/2/2_1 ... engt.shtml
almost every compound exercise can be improved by adding isolation exercises into training, and running is just that, a compound exercise. many areas work together, so yes you should practice running as a whole, but do not neglect the fact that each part is different, and are rarely all equal in performance.