Couldn't you combine both systems relatively easily to get the best of both worlds?

Something like this: Imagine a standard central heating system: Radiators connected to a boiler through a water circuit.

Except now, the boiler's exhaust is additionally led through an oven-stove-like stone structure that acts as a "heat storage". The water piping goes through both the boiler and the stone structure.

You retain the flexibility and speed of central heating: If you want to heat up a room quickly, the boiler can heat up the water directly; if you want to cool a room down, disconnect the radiator. However, at the same time, the stone structure will store heat long-term and will hopefully allow the boiler to run for shorter periods of time.

I gotta admit, it's less exciting than an actual oven stove though, as it reduces the principle from "radically different ways of heating" to "minor technical improvement of boiler systems".

There might also be the issue that heat transfer from the stone structure happens indirectly again, which might make the system less efficient than an actual oven-stove.