"Think about the example of a piece of real property (someone's home) being lien against, the owner being evicted until he pays the back property tax allegedly due."

Equity deals with trust law. Trusts consists of fiduciaries and beneficiaries. Property is put into the name of the trust and is used for the benefit of the beneficiaries. Government officers and employees are the fiduciaries and the people are the beneficiaries (actually the settlor / beneficiaries). The land and property controlled by the trust (government) is not the land and property owned by the people. The people have retained their right to own property outside of the trust. The trust has no interest in the private land and property of the people, and as fiduciaries, government officers act against the interest of the people by placing a lien on the private property of the people. Equity does involve judicial discretion, but that discretion cannot be abused. The inalienable rights of the people cannot be encumbered by government. Fiduciaries owe the duty of obedience to the people, and that obedience is to follow the express trust document, the constitution of the state.