"Few" and "a few" are significantly different in grammar and meaning.
"A few" is neutral: it simply refers to a small number of whatever, without suggesting any expectations.
"Few" triggers negative polarity expressions (such as "any" and "yet"), and emphasises the smallness of the number, and suggests that a larger number might have been expected.
A few people have registered.
A few people have an idea what's going on.
Contrast this with:
Few people have registered yet.
Few people have any idea what's going on.
both of which are emphasising that the number of people is small.
A few with negative polarity items is not grammatical:
*A few people have registered yet.
*A few people have any idea what's going on.
There is no real answer to your question: like most "why" or "what is the reason" questions about language, the only answer is "because that's the way it is".