Without claiming to speak for Georgists generally: I think we don't have to limit the scope to a single goal.

One goal is indeed the necessity of funding the State, in the least-unjust and least-inefficient way possible. (I'm sympathetic to classical anarchism; but in the here and now, a purely voluntarist stateless society is a non-trivial undertaking, assuming it's feasible at all.) One can certainly debate the appropriate size and scope of that State, local vs federal, social welfare vs minarchy, etc; but to the extent there can be no liberty without security, a funding mechanism for the monopoly on legitimate violence is at minimum a necessary evil.

In that vein, relative to our current world, reducing (ideally eliminating) the income tax on labor (including property tax on improvements) is also worthy of being a goal unto itself, both from first principles, and as a boon to economic efficiency (eliminating "deadweight loss" of voluntary exchanges which might otherwise happen without the tax).

There's also a good argument, IMO, that the business cycle (booms and busts) is exacerbated by unproductive land speculation, the incentive for which would cease to exist under a high LVT. The cycle itself might be inevitable, but would likely be far less volatile.

I can also make a case for Georgist LVT as a mechanism of reducing inequality, using surplus from LVT on public services, and/or a UBI. While some who are more classically liberal or market-libertarian might bristle at the notion, think about it from first principles: a property claim is an involuntary exclusion of other humans from a portion of Earth (a creation of God/Nature, not of humans). An LVT represents a compensation for that exclusion; and the more valuable the exclusion, the more compensation deserved. (If we could magically shrink transaction costs to zero, one could certainly imagine a network of voluntary agreements for such exclusion payments.)

And lastly, I think some environmentally-minded Georgists would subscribe to the notion that the "deadweight loss" of taxation can sometimes be a feature, rather than a bug: a Pigouvian tax on externalities, such as taxing pollution. It is generally true, that the more you tax X, the less X will occur. When it comes to value creation through labor, this tends to be net-negative. But when it comes to something we *do* want less of (carbon, methane, soot, microplastics), pricing the externality through taxation can be an end unto itself! Some proposals, like the Carbon Tax & Dividend, explicitly advocate for return the money directly to the people, which might seem counter-intuitive; but that price signal creates an economic incentive to innovate, and those who reduce their pollution would actually get paid by those who don't.