Pricing is the main issue. API's usually aren't free, especially as you grow your business. Most consumers don't have a problem with their main apps; if you can't create this service for free or a super low cost, it's hard to get buy-in.
Most apps also want to make it easy for you to do repetitive tasks quickly. Doordash has a "recent orders" section where I can tap to reorder. That's pretty seamless.
This general idea holds across most large consumer apps: if something is done repetitively, the app has a way to make that process faster. As such, a personal assistant only becomes useful for edge cases like "ordering from a new restaurant where you already know what you want and know that it's on Doordash."
Even in your example of "book a tennis court at 6," you might run into issues. What if the court is booked at 6? I might have secondary times in mind, or I might be willing to settle for a 45 minute session if it's available. All of this is easier to deal with using a calendar interface. And what if different times cost different amounts of money? I wouldn't necessarily know what amount that hour at 6 would cost, and that may matter to me.
Poimt being that these apps work well for one thing: tasks that you do repetitively many times, that aren't sped up by the original app itself, and where things won't change. That ends up being a pretty limited usecase, even if you can keep the service cheap.