It has not been clarified so this is just speculation:
If the Queen of Thorns had carried the poison into the wedding on herself then there is a small chance that a trace might get left on her somehow and she might be implicated.
Imagine the political catastrophe if the Tyrells were implicated in regicide via physical evidence. The family name and all of their plans would be in ruins and war would be the probably result. Even a small chance of this is too much.
However, Littlefinger knew that Sansa would vanish without a trace before any actual investigation started (he had arranged it via Dontos) and hence no one would could reliably know who was responsible and it would cause trouble.
Littlefinger likes causing trouble as it allows him to play his game more easily. If Tyrion had not been appointed cup bearer and humiliated by Joffrey then he would not have been so obvious a suspect so who would have got blamed? Anyone? Everyone?
Even if they suspected Sansa they would never be able to find her to prove anything so Cersei's desire for revenge would probably switch to another target.
Potential alliances would have shattered and division would have sprung up. Littlefinger would have played both sides like an ambidextrous fiddler who was also an expert juggler.