Can you give examples of how this is true? I feel like the main government spending that made me more productive was some transit spending before I was born and their education spending. I feel like most government services aren't this.
Even things like health care, which arguably keeps me healthy enough to work isn't distributed in any sort of uniform way so the productivity increase from it isn't likely to match the land value tax increase.
I think there are a lot of things that can increase land value 22%. I think some of them might even raise average wages 22%. I think almost none of them will raise each individual wage by 22%.