First of all I said by the end of his career.
Actually...you included this nugget as part of your OP
He already might have a strong case for it (greatest playoff WR) up there with Rice and Fitzgerald.
1200 fewer yards / 17 fewer TDs / 1 fewer SB ring than Rice......That's your strong case?
While perhaps it's unlikely that he'll surpass Rice, How many big clutch catches does Rice have in the playoffs by memory? Most of his were in blowouts although that isn't quite his fault.
Rice scored 11 playoff TDs combined in SF's '88 & '89 SB campaigns. (6 more than JE's career total)
Some might argue that San Francisco was blowing teams out in large part because of Jerry Rice 's domination. Minimizing Rice's dominance in that era based on your fleeting memory of signature moments...a peculiar way to support an argument.
We're talking about all around greatness, not just production. Edelman has a long list of great playoff moments already.
I'm not posting in order to minimize Edelman's value to NE and their playoff successes.....but lets get real. JE is NE's go-to / move-the-chains WR between the 20's and a useful redzone option but certainly not option 1 or 2 (TE, RB)
One more playoff TD and JE will reach David Givens heights.
And because you value total catches so much, remember the game is very different today than decades ago. Brady has averaged close to 40 passes / playoff game over his career while Montana averaged about 31 / playoff game. And who has benefitted from the surplus in passing during this NE run of excellence...the NE slot receiver, whether it was Brown, Welker, or Edelman.....to me....they all seem interchangeable. Glad we have 'em....and BB has proven he can discover the next immortal anytime he needs to.
Edit: One last point. While its true SF dominated the AFC representatives in their SBs, let's not forget the gauntlet of NFC powerhouses that thrived in that era. With some of the greatest teams in NFL history fighting for NFC domination... Giants, Chicago, Dallas, and SF.....and the arms war that was taking place with high priced defensive mercenaries jumping around from team to team....the true NFL championship was played two Sundays before the SB.....and Rice was a major difference maker. NE has never had to face such a gauntlet