I remember the early days of cell phones well – the wife had a company-provided Motorola brick phone, which was a wonder of its time (and cost around $6000, IIRC). But the only other kind of cell phone I recall from the time was the “car phone”, which was permanently mounted in the car, and wired to a distinctive outside antenna. I had to Google “bag phone”. If I ever saw such a thing, I must have forgotten. They couldn’t have been all that common, at least around here. OTOH, I tend to forget a lot of things! 
I would imagine they were also cheaper, since they didn’t need the leading-edge miniaturization of the handheld brick phones.