They want to use this tech to eventually land rockets on other planets so the rocket needs to be able to land upright. Short term it might be easier to land on inflatables but they're looking at the bigger picture.
The utility here is not really landing on other planets, but instead the order of magnitude decrease in launch costs if they don't have to build a new first stage for every launch.
This could theoretically be achieved by either means. The question was specifically why a vertical landing is favoured over a cushioned inflatable landing.
Musk has stated in the past that they're looking to eventually use this tech to create rockets which can be used on Mars, hence why parachutes and inflatables are out of the question.
No, its just not possible to maintain the integrity of the rocket if you're going to somehow lay it down on an inflatable. How could an inflatable withstand the temperature of the firing engines?