what is obviously clear is that the figures I gave are a 'best' case estimate, and in actual
practice, the v.reg will run even hotter yet.
What you have assumed is that the thermal resistance from the case to ambient is 0 (aka an infinitely large heatsink).
Most sot223 chips have no heatsink other than a puny copper trace on the board. You can check the datasheet to see the j-to-a thermal resistance of the package and the math is easy.
In general, it is good to assume 100c/w thermal resistance for those devices. That means in reality a 0.5w power dissipation is the most you should put on such a device.
Those 1amp ratings for such small packages are simply meaningless.