Here's a case in which we can do without the indefintie article: "Boston has a lot of history". Here we are talking about "history in general", not any particular type of history, such as "a long history", as in "Egypt is a country with a long history".
Consider this: He's a doctor. Why do we have to say "a doctor"? Why can't we just say "he's doctor"? In English, we first have to recognize that he is "one" doctor of many other doctors. We do this with the indefinite article. One is left to simply understand, or believe, that he is one doctor of many in languages that don't utilize indefinite articles in this way.
In English, if one says, "he's doctor", it's quite possible for the listener to think, or wonder, "he's doctor? doctor who? What's his name?" He's Doctor Louis. One would likely not think this, but the potential is there, given how the grammar functions - the purpose of the indefinite article in English.
Now, he's not one doctor of many doctors. In this case, one could say, "he's the doctor I've been going to for the past two years", for example.
Does this help you make sense of the indefinite article in English? I hope so.