I would argue the primary benefit of having an API even if not made public is that it will encourage better architecture , design, and development making the product more maintainable over the long run.
It also means you can scale if you ever do need to add a customer that wants to make use of an API.
Saying not to do an API because customers don't want it is similar to not using source control because you're the only developer.
An architecture is good if it is serving your business’ needs. My company makes $13 billion a year off of garbage architecture. If we completely re-engineered it to be perfect, we’d probably still make the same amount of money, it would just cost us hundreds of millions of dollars to do it (actually, we tried and wasted about $300mil).
Is having an unnecessary API really better architecture though? It adds quite a bit of complexity and there are other ways to address separation of concerns.
Depends on how big your team is. If it's just you and you feel like you dont need one then dont.
If its 3 teams of 10 then an API is extremely helpful. It's a great way to frame conversations in something beyond personal preference.
It also means you can scale if you ever do need to add a customer that wants to make use of an API.
Saying not to do an API because customers don't want it is similar to not using source control because you're the only developer.