Whatever the default search target for travel stay is, if there is one, will probably determine a large percent of what users will simply stick to using without bothering to change it to another preference, since they may not know better. This default does leave an opportunity for some companies to have an edge over others, and potentially pay to make it so.

Not if there's only one intergration.

The problem with third party integration is that you're going to end up getting a bunch of duplicate "skills", to use Alexa terminology, of varying quality and capability. It's the App Store problem, and bot store problem all over again.