Yes, the point in your edit, is true.
For your main question, the answer is simple. It is not necessary to say "go to the hospital" or "go on the holiday", when talking in a general sense. Use of the word 'the', means that the sentence is in a particular sense. A reference to one, particular example. "go to the hospital" will mean going to one, particular hospital.
If what you mean is going to a hospital generally, for example talking about an injury that happened to you many years ago and an ambulance was called; then saying "the hospital", will have a different meaning.
I noticed that it is Americans who will speak like that. This sounds odd and unnecessary to me, as a British person. I have not heard any British people speak like that.
This can cause misunderstanding. I remember an example of this, when I was talking to an American friend. They mentioned an incident in which their neighbour had an accident and an ambulance was called. They said the neighbour was taken "to the hospital" and came home the next day. I asked which hospital and they stopped talking for a moment. They looked confused and asked why I would ask that, considering that I don't live near them and therefore would not be familiar with it. After explaining that this not how British people speak, they realised.
If what you mean is one, particular example, like going to a particular hospital or a particular school that you have referred to by name; then, saying "going to the hospital" or "going to the school', will make sense.
Basically, the word 'the', is not necessary in sentences that are in the general sense. The, is used when referring to something in a particular sense.