Have each citizen pay the service provider directly for the portion of the service they use, at the time of consumption. Allow the service provider to charge an administrative tax on top of the service tax to cover expenses.

This policy will have problems, "toll sidewalks" being one of the easier ones. But it solves a lot of big problems. How well does it satisfy your goals?

Fair: This is very hard to pin down. People who pay more will argue that any system is unfair, and people who pay less will argue that it is fair. Your goal, to "avoid situations where some pay taxes while other's don't" is tricky. Smokers pay tobacco tax, non-smokers don't. Many "loopholes" are created for good reasons: charities don't pay property tax, people with fuel-efficient cars don't pay a gas guzzler tax.

With my proposal, people who use services pay the taxes that provide the services, proportional to how much they use. No one pays for services they don't use. That is about as close to a dictionary definition of "fair" as I can imagine.

Progressive: It's a consumption tax, so citizens who consume more services will pay more, and it's reasonable to suppose that citizens who earn more will consume more.

Simple: No accountant or lawyer needed. No tax infrastructure. No tax code. Anyone can choose to provide a service, and they are automatically granted a permanent, free, tax-collector license. No paperwork.