>But homeowners would likely be willing to share value too

No, they wouldn't. That is why property tax rates (and hence land value tax rates) have so many laws capping them and otherwise limiting them for all the important voting blocs (old people, military, big business, etc).

See California prop 13, that voters passed. See Oregon measure 5 and 50, also passed by voters. And politicians wouldn't dare touch these.

>In American cities, there is an issue with value capture. One party creates the value (in this case retailers), another party (landowners or homeowners) captures it.

This phenomenon is not restricted to American cities. It will broadly exist in all human societies with flattened or top heavy population age histograms. The old are the most populous and knowledgeable (and motivated) to structure society so that the non working (themselves) can capture the most value. Hence, the popularity of earned income tax instead of marginal land value tax rates. The goals of the wealthy and the old (and the ones with aspirations to be wealthy) align to support rent seeking policy.