When I was growing up, almost all fire engines had open cabs, very few had a cab with a roof, and if they did, they were usually fire apparatus that were built on commercial truck chassis. On ladder trucks like this American la France in the photo, an open cab is much preferred in spotting the ladder truck, the driver only has to look up to see if it's a good place to raise the Arial Ladder without running into interference with power lines, etc.
Jack Parr is known for his line "I kid you not". Which then ,soon became the preferred, "I shit you not"
I spend a lot of time around firemen, almost on a daily basis. Fire apparatus have changed over the years. One of the main reasons that most fire departments in big cities went for closed rather than open cabs were the riots in the 1960's, where firemen were being shot at or had rocks thrown at them. In Los Angeles, it was the Watts Riots that pushed the switch from open cabs to enclosed cabs. Even the ladder trucks have closed cabs for the guy on the tiller, the fireman that steers the back of the aerial ladder truck. We have gone from this... ...to this.
ah...what a happy couple we have here...and the kid in the back ground is practicing to be a professional photo bomber later in life