Seems an arbitrary way to measure this... even though your numbers back me up.
How many weeks was he not a WR1 and vice versa.
Now do that for the other WR1s.
I'm betting he had the most weeks as a non WR1 over the last 2 years.  Maybe the most weeks as a top 5 the last 2 years as well.
		
		
	 
Assume you are suggesting that, of all players who finished ranked as a WR1, Cooks had the most weeks where he did not rank as a WR1, where WR1 is defined as top 12 WR scores for the week.
I would point out that this is also arbitrary. The cutoff between WR12 and WR13 in a given week could be 0.1 point, e.g. 19.2 points to 19.1 points. Thus, that cutoff does not always represent real value.
However, I was interested enough to look at this for the 2016 season (regular season weeks 1-17). I used scores in one of my standard PPR leagues. There were 80 players who had a top 12 weekly score at least once. Here they are, with their number of top 12 weeks:
8    Beckham, Odell NYG WR
	8    Brown, Antonio PIT WR - 15 games
	8    Evans, Mike TBB WR
	8    Jones, Julio ATL WR - 14 games
	7    Nelson, Jordy GBP WR
	6    Hilton, T.Y. IND WR
	5    Baldwin, Doug SEA WR
	5    Bryant, Dez DAL WR
	5    Landry, Jarvis MIA WR
	5    Meredith, Cameron CHI WR
	5    Tate, Golden DET WR
4    Adams, Davante GBP WR
	4    Benjamin, Kelvin CAR WR
	4    Cooper, Amari OAK WR
	4    Diggs, Stefon MIN WR
4    Green, A.J. CIN WR - 10 games
	4    Robinson, Allen JAC WR
	4    Sanders, Emmanuel DEN WR
	4    Thomas, Demaryius DEN WR
4    Thomas, Michael NOS WR (R) - 15 games
	3    Cooks, Brandin NOS WR
	3    Crabtree, Michael OAK WR
3    Fitzgerald, Larry ARI WR
	3    Inman, Dontrelle SDC WR
	3    LaFell, Brandon CIN WR
	3    Matthews, Rishard TEN WR
	3    Montgomery, Ty GBP WR
	3    Smith, Steve FA WR
	3    Thielen, Adam MIN WR
	3    Wallace, Mike BAL WR
	2    Austin, Tavon RAM WR
	2    Brown, John ARI WR
	2    Crowder, Jamison WAS WR
	2    Edelman, Julian NEP WR
	2    Fuller, Will HOU WR (R)
	2    Ginn Jr., Ted CAR WR
	2    Hill, Tyreek KCC WR (R)
	2    Hopkins, DeAndre HOU WR
	2    Jones, Marvin DET WR
	2    Lockett, Tyler SEA WR
	2    Matthews, Jordan PHI WR
	2    Nelson, J.J. ARI WR
	2    Pryor, Terrelle CLE WR
	2    Sanu, Mohamed ATL WR
	2    Snead, Willie NOS WR
	2    Stills, Kenny MIA WR
	2    Williams, Tyrell SDC WR
	2    Wright, Kendall TEN WR
	1    Allison, Geronimo GBP WR (R)
	1    Amendola, Danny NEP WR
	1    Beasley, Cole DAL WR
	1    Boldin, Anquan DET WR
	1    Boyd, Tyler CIN WR (R)
	1    Britt, Kenny RAM WR
	1    Coates, Sammie PIT WR
	1    Cobb, Randall GBP WR
	1    Coleman, Corey CLE WR (R)
	1    Decker, Eric NYJ WR
	1    Enunwa, Quincy NYJ WR
	1    Gabriel, Taylor ATL WR
	1    Garcon, Pierre WAS WR
	1    Hawkins, Andrew CLE WR
	1    Hogan, Chris NEP WR
	1    Humphries, Adam TBB WR
	1    Hurns, Allen JAC WR
	1    Jackson, DeSean WAS WR
	1    Jeffery, Alshon CHI WR
	1    Kerley, Jeremy SFO WR
	1    Marshall, Brandon NYJ WR
	1    Mitchell, Malcolm NEP WR (R)
	1    Parker, DeVante MIA WR
	1    Quick, Brian RAM WR
	1    Rogers, Eli PIT WR
	1    Royal, Eddie CHI WR
	1    Shepard, Sterling NYG WR (R)
	1    Thompson, Deonte CHI WR
	1    Watkins, Sammy BUF WR
	1    Wilson, Albert KCC WR
	1    Wilson, Marquess CHI WR
	1    Woods, Robert BUF WR
The top 12 in ppg for the season are bolded. I noted number of games played for some notable players but not all.
Cooks and Fitz tied at the lowest number of top 12 weekly scores, with 3 each. Take a look at the guys who finished with 4-5 such games. How many would you rather have than Cooks?