Very technically, it IS a turn based strategy game. You have maneuver (deciding which horrible monster to throw into the frey in a given moment), attack selection, and force makeup (determining which horrible monsters will confer the highest probability of winning any expected encounter). That said, it does not meet the specification put forth by the OP.
I would say that a turn based strategy game could work just fine, but such a thing would almost certainly require dramatically reducing the number of pokemon available. As it stands there are piles of pokemon that are little more than pokedex filler garbage that would need to be thinned, and a wide number of pokemon that share similar skillsets. Moreover, distinct differences would need to be enabled such as differing rates of movement, general ranges for attacks and so forth. In short, while the resulting game may take place in the pokemon universe, the central mechanics and ideas that have carried the franchise forward would need to be dramatically altered. In general, the series has not met much success when it comes to radical change. Indeed, so opposed to such nonsense is pokemon that the most recent releases are simply the game boy color games re-issued with better graphics on a different system.