Coming late to the party as I have been very busy elsewhere in RL but...
I do agree that an "Olympic programme" is either (a) any programme skated at the Olympics, or (b) the one that becomes truly iconic, drawing in the public, remembered and returned to for years, and constituting a true "business card" of the sport, its most precious exhibit, loved and admired, as Olympics is when FS gets most exposure from the general public perspective.
I also agree with
TallyT that the Olympics site is the best resource for this, and this is one of these occasions when the public's choices should be given most consideration. Therefore, a perfect Olympic programme is the one that is presented at Olympics and wildly loved by the public.
So here is the list of Top 15 most viewed Olympic figure skating programmes from the Olympics site which seems to be a fair selection for the last 15 years (I understand older iconic programmes, like Bolero, Carmen or Kalinka-Malinka, do not get viewed that much as they mostly come from a pre-YouTube era,):
1. Yuzuru Hanyu - Seimei FS - Pyeongchang 2018 - 42.6 million (views)
2. Savchenko/Massot - La Terre Vue Du Ciel FS - Pyeongchang 2018 - 42 million
I agree the second one does not really get mentioned that much and may come as a surprise to some but.. here you go!
Now here's a huge gap from the top two followed by:
3. Virtue/Moir - Moulin Rouge FS - Pyeongchang 2018 - 25.4 mln
4. Yulia Lipnitskaya - Schindler's List FS - Sochi 2014 Team Event - 24.4 mln
5. Davis/ White - Indian Folk Dance FS - Vancouver 2010 - 18.5 mln
6. Yuzuru Hanyu - Parisienne Walkways SP - Sochi 2014 - 16.4 mln
7. Alina Zagitova - Don Quixote FS - Pyeongchang 2018 - 14.5 mln
8. Yuna Kim - Concerto in G by Gershwin FS - Vancouver 2010 - 12.5 mln
9. Volosozhar / Trankow - Jesus Christ Superstar FS - Sochi 2014 - 11.7 mln
10. Yuna Kim - Adios Nonino FS - Sochi 2014 - 10 mln
11. Suzaki/Kihara - Yuri on Ice SP - Pyeongchang 2018 - 8.9 mln
12. Yuzuru Hanyu - Chopin's Ballade No 1 SP - Pyeongchang 2018 - 8.3 mln
13. Virtue/Moir - Stay by Rihanna (exhibition!!!) - Sochi 2014 - 7.6 mln
14. Alina Zagitova - Black Swan SP - Pyeongchang 2018 - 7.2 mln
15. Yuna Kim - James Bond Medley SP - Vancouver 2010 - 7 mln
Now, this is what the current crop could be looking up to, and what they need to match if they want to break into the top of the tops

Any surprises? Any conclusions?
PS The quiet hero of this "most watched Olympic hits" list is ... Brian Orser. You can see him in 5 of these Top 15 videos as he's the coach behind 5 of those 15 iconic programmes!!! This makes for one third! Quite a result, too!!!
And here are the two winners!