I have a question about voltaic cells. Let's say I dip Zn and Cu rods in a beaker of acid. My book says that Zn donates 2 electrons that travel through the circuit and to the Cu electrode. Cu electrode gives the electrons to H+ ions in solution.

Now my question is, why does the 2 electrons produced by Zn have to travel around the circuit? The H+ ions are surrounding the Zn electrode too. So the 2 electrons can go to the H+ ions near the Zn electrode instead of travelling through the entire circuit right?
I mean as soon as the 2 electrons are produced, they can be picked up by nearby H+ ions. So why do they need to travel all the way from zn electrode to the wire connecting zn and cu electrodes to the cu electrode and finally to the H+ ions?

Any help would be appreciated.