Your Argument about the large delays caused by convoys over independent sailings are refuted in the Admiralty staff college document
you are comparing the efficiency of peace time sailings to war time convoy operations. The correct comparison is between war time independent routing and war time convoys.
you are pretending that ships still stayed on peacetime schedules During the war and that no ship delayed leaving harbour when it had news of U Boat activity in the vicinity.
page 17 of the PDF
http://www.ibiblio.org/hyperwar/NHC/NewPDFs/UK/UK, Defeat-of-Enemy-Attack-on-Shipping1939-1945.pdf
it’s in the Chapter lessons of the first world war.
to Quote “ What was not taken into account were the crippling delays experienced in war time by the hold up and routing of independently routed ships. These delays were as strong a reason for the introduction of convoy in 1917 as the need to reduce actual Sinkings”
Two problems. Not actually data, just an opinion. Second, much more important problem is that the UK deliberately fudge the data in the WW1 analysis to reduce the number of subs built by other nations and odds of second major merchant war. You keep quoting INTENTIONALLY incorrect summaries. You somehow keep having some single ships occassionally have delays departing or waiting for a dock to routinely having 10's of ships hang around for days. It is the equivalent issue of the occassional issues that I have traveling on weekend to regular, weekday traffic jams. I know this is hard to accept, but these sources you quote are of the same reliability of a late Nazi era news clip.
Now lets look at some numbers. Famous convoy. HX 127, Halifax to Liverpool 2593 nautical miles. May 16th to June 2, 17 days. 408 hours. Speed. 6.4 knots average progression if heading straight.
HX 117 - 19 days, speed around 6 knots.
HX 107, 26 days. Speed. 624 hours 4.2 knots.
https://www.warsailors.com/convoys/hx127.html
Now these are the fast convoys, Liberty ships probably run at near 11 if straight which is a 10 day trip, roughly speaking.
So lets do an example of one of the 10-11 knot ships in HX 127. If run independently, it takes 2-3 days to load, 10 day trip, 2-3 unload, 10 day trip. Round trip every 25 days. If we take HX 117, mid range before port congestion, it is 2-3 load, 19 day trip, 2-3 unload, 19 day trip. Shipment about every 42 days, round trip. Take 25 times 1.5 (1/3 loss), you get 37 day round trip.
See how not only can I explain the logic, I can document with multiple real convoys with live data. 1/3 loss of capacity is a good estimate.
And just so you don't get indirect routing like they ran to Iceland coast, 9 extra days is around 2200 nautical miles detour. The detour would be leaving Halifax, going to Charleston South Carolina, then going to Lisbon, then going to Liverpool.
And just so you understand it was not the speed of the ships, SC-100 (slower convoy) only took 16 days to get from Halifax to Liverpool.