Type marksman in the "Insert a champion icon" tool

I think you mean "Select Marksman from the dropdown", because the filter does not sort by roles, only by name (typing Marksman would not show anything). Because it's from the dropdown, if you read it before you click it you might notice that it says Primary Role. Marksman is Azir's Secondary Role, so he won't show up in that either.

You're simply a bit confused; Azir is Primary Mage, Secondary Marksman. The "Insert Champion Icon" does not discriminate, it will search for name, role, and other filters.

For a better early game and casting, I'd say it's more buff than it is nerf.