For example, it could just be that ML is not your business. If you're a image hosting platform, you don't necessarily want to build your own NSFW image checker. There's no harm in leveraging something else out there that works great, assuming that you can bankroll it.
Alternatively it can be used as a stop-gap. You're in the middle of implementing your own ML system (or planning to), but you can use a 3rd party to fill the gap until you're ready to go live with your own version.
This is also a great way to test new features and see if users respond to it.
In my opinion it boils down to if either you need to own the model, or guarantee the quality of it, then perhaps you should consider owning it yourself. Otherwise, it's fine to consider using a third party.