I do keep three seconds separation most of the time. If possible I engage traffic aware cruise control set to maximum separation for just that purpose. People do cut in but not often; what would be the point of cutting in between two vehicles that are both going slower than your desired speed?

Also perhaps I should have made it clear that I am in Europe where one is expected and required to drive in the outermost (rightmost except in UK and Ireland) lane unless overtaking so the only time anyone would 'cut in' between my car and the one in front is when they are entering a motorway.