Could Mars' ancient tectonic activity have ceased due to its oceans having been composed of sulphuric acid, which warmed up and evaporated due to the Theia event as ice chunks landed on its surface? Strongly conductive liquid sulphuric acid on early Mars' surface could have been responsible for generating its core spin causing tectonic action which then all died off as a result of its oceans evaporating and thus removing the conductivity responsible for the core spin, whereas Earth's oceans didn't evaporate (because they are water) so can phase to ice ages to prevent overheating.
Why else would Mars have evidence of ancient alternately polarised extrusion from now ceased tectonic activity?
First, tectonic activity have not ceased on Mars, although the planet is in a "stagnant lid" stage, which represents the last stage before a body becomes tectonically dead. See the answer to Is there convection in Mars' mantle?
Second, tectonic activity is caused by internal heat. As a planet gradually loses its internal heat, tectonic activity slows down, until it eventually stops. There is no need for more convoluted explanations.