In principle, yes, but maybe more often.
I think that since the 80s we have come to a better understanding of the role of longer runs and tempo work too. You might be even better off spacing things out into a 3 week cycle and including a week with a 4-5 mile tempo run, a decent long run and 2-3 straight easy days (plus some strides or easy relaxed 100s/200s) every third week - sort of a "low lactate week".
Also, the other poster is right that you can mix paces too. If you haven't done 5k pace or 800 pace for a couple of weeks, do half of each.
Presumably you have some races available to you - even if it's pre-season road 5ks, which are great training and better than any 5k track session - so fit the sessions into the gaps, rather than being dictated to by a 2 week cycle.
I use 5-pace as a mental checklist to say "what paces haven't I trained at lately?".
I'm pretty sure nobody ever did it. Frank is a brilliant motivator, a great scholar of the sport, and a deep thinker, but sometimes he gets a little carried away (in fact he can spout some real nonsense at trackside, but it always sounds good at the time!). Apparently Tim Hutchings (his star pupil, 4th place in LA 5000) attempted something like this and decided about 3 days in to space the sessions out a bit further. Certainly when Peter Coe corresponded with him, he got a conventional 3-sessions-per-week version like yours more than 30 years ago.
I think this is one case where he either wrote some stuff down a bit too late at night, or maybe dictated it in the pub to a keen Serpentine member who got it wrong, and it accidentally got preserved. Such are the interwebs ;-)
I don't get to Battersea Park any more but I'm seeing some people who train with him this Saturday - I'll ask them to ask him.