There's no reason to care if a tax is progressive.
The thing to care about is whether the government is redistributing wealth in a desired way.
Progressive taxes are one way to redistribute wealth to the less wealthy. Payments are another.
If you want a more progressive system in a LVT world, double the tax rate and then send people checks.
Whether those transfer payments are via taxes, payments, or services is not essential for the goal.
If you encode it in tax rates, you are subsidizing behavior that you are trying to deincentivize via taxes, which is unfortunate.
The idea of LVT or other taxes on externalities is to tax behavior you want to prevent. That's why we should tax the capture of land, the pollution of the environment, adding traffic to a transportation system, etc. That's why it's unfortunate to tax things like "making your house nicer" or "converting a parking lot to a veterinarian office" or "hiring another employee". You wouldn't sent checks to someone because they let their house decay or they fired someone, so why would you give them a tax break?
The point of the transfer system is to help people who need help, right? Not to discourage things we want to happen.
I don’t want to get sidetracked on whether or not the incentives are good, or even whether a regressive tax is bad. (Though I admit I sidetracked with my comment above.) The question is why a land value tax is progressive in a modern industrialised country with a services-based economy?