Couldn't Varys or LF have set up Pycelle in ACOK?

[Chebyshov]

I'm in the middle of my first reread, and the part where Tyrion tells Pycelle, LF, and Varys all different plans to figure out which one is informing on Cersei is seeming really dumb this time around.

After proposing fake plans with Pycelle and LF, Tyrion meets with LF, who begins their conversation by saying:

“You are a cruel man, to make the Grand Maester squirm so,” the eunuch scolded. “The man cannot abide a secret.”

“Is that a crow I hear, calling the raven black? Or would you sooner not hear what I’ve proposed to Doran Martell?”

Varys giggled. “Perhaps my little birds have told me.”

So off the bat Varys indicates that Pycelle can't keep a secret and it's possible his "birds" told him what this was.

Then, later in the conversation, the following exchange happens, indicating that Varys had complete knowledge of what Tyrion told LF too:

Varys smiled his slimiest smile. “Which one will you give him, I wonder?”

Tyrion sighed. “You know, don’t you?”

“Since you put it that way-yes. Tommen. You could scarcely offer Myrcella to Doran Martell and Lysa Arryn both.”

“Remind me never to play these guessing games with you again. You cheat."

So right there, Varys straight-up tells Tyrion that he overheard him promising Myrcella to Lysa (the LF conversation).

And to cap it all, Tyrion then explains to Varys why he's doing what he's doing.

“What Cersei does not know will never hurt me.”

“And if Her Grace were to discover your intentions before your plans are ripe?”

“Why,” he said, “then I would know the man who told her to be my certain enemy.” And when Varys giggled, he thought, Three.

So based on the fact that Varys 1) Demonstrated his knowledge of Tyrion's plans and 2) Tyrion directly told Varys that whichever plan Cersei overhears will point him to the informant, couldn't Varys could have easily set up Pycelle? Or even LF, assuming that he has the ability to gather information too?

I don't really think either did; Varys would likely prefer to set up LF. But Tyrion's self-congratulatory attitude here seems out of place. Especially given that he knows Varys has overhead him.

[TheBlackFlame]

Well none of that really matters now does it. Pycelle is literally a dead end.