Question about reaction in battery

I made a battery like this.  



$\ce{(-)Al|HCl,CuSO4|Cu(+)}$  



By piling up 6 battery of this(actually I made this using 10 yen and 1 yen coins:10yen coin is Cu and 1 yen coin is Al.) I could turn on an LED light.
The plausible reactions taking place at the cathode and the anode are as follows.  



Anode: $\ce{Al ->Al^3+ + 3e^-}$  

Cathode:$\ce{Cu^2+ +2e^- -> Cu}$ and $\ce{2H^+ + 2e^- -> H2}$
[![enter image description here](https://i.stack.imgur.com/athiW.png)](https://i.stack.imgur.com/athiW.png)


I have an question here. Why doesn't all the electrons released from Al reduce $\ce{Cu^2+}$ or $\ce{H^+}$ immediately at the anode site?


<https://cs.kus.hokkyodai.ac.jp/tancyou/vol.40/enn.htm>
  
This url shows the battery on which mine based.
But I used paper wetted with HCl which contains CuSO4 , not NaCl saturated water like shown in the URL and picture above.


