Because it has never been Tyrion's blade. You said despite the damning evidence but what evidence? Are we really trusting Littlefinger?
That's what Tyrion said in his defense:
It was not my dagger. How many times must I swear to that? Lady Stark, whatever you may believe of me, I am not a stupid man. Only a fool would arm a common footpad with his own blade.- source
And in "The Dragon and the Wolf":
ARYA: You told our mother this knife belonged to Tyrion Lannister. But that was another one of your lies. It was yours.
And he said nothing in defense about dagger.
And it's already been discussed who sent the killer in similar question:
Who sent the assassin to kill Bran Stark?
So most probably behind the scenes Joffrey contacted Littlefinger for this murder attempt and as he is, he made this convoluted plot.
