Courts grant state officials and private citizens license to disobey or obstruct the Executive leadership. So if your bureaucrats aren't on board, a court ruling can let them throw up their hands in helplessness when you tell them to comply.

Similarly, it can enable them to act fearlessly when they are enthusiastic advocates of the ruling. Abolishing Roe gives the local pig brigade license to assault and arrest pregnant women with abandon. It grants private groups license to engage in domestic terrorism under the guise of enforcing the law. And it mutes public criticism of the above, as you're now advocating criminality in opposition to the law.

For a society dead set against a decision, the SCOTUS is powerless. But consider how Eisenhower unleashed the power of the state after Brown v. Board, as it granted him license to persecute opposition party rivals. The real underlying power of the courts is to grant credible public legitimacy. That goes a long way towards empowering radicals and reactionaries in turn.