Zee just seems so much more logical to me.

Why?

The names of the letters are just names. Call it Zee, Zed or Nigel if you like. I can't see where logic enters into it at all. If the alphabet were logical maybe it should go

Ay-ee, Bee, See, Dee, Ee, Fee, Gee, Hee, Eye-ee, Jee, Kee, Lee, Mee, Nee, Oh-ee, Pee, Quee, Ree, See, Tee, You-ee, Vee, Wee, Ex-ee, Yee, Zee

I think I shall try to introduce this new system.

I guess that's the Alpha and the Omega of it.

Isn’t that the Chinese version of English alphabet? (Or is it non-PC for me even to mention the stereotype?)

Nah, Pee Quee Ree was a Korean politician.