We didn't have one like this, but it seemed like most of my friends' parents did when I was little. Somewhat surprisingly for someone who was obsessed with records and record players (and fond of the radio) from a very early age, there was something about these that I instinctively disliked - they seemed clunky, and generally didn't sound as good to my ears as my brother's portable little General Electric record player with speakers built into the lid (especially after he extracted the speakers from the lid and put them in opposite corners of his bedroom).
My family did have one of these things, which we referred to as "the hi-fi":
The top lifted up and there was a record player and radio there. Monophonic. Oddly, I don't remember the radio getting used much. It was decidedly less than hi-fi, but it was "my" first record player, and even before I could walk I would crawl over and park myself in front of it if one of my older brothers put on something groovy.
Many years later, Mom told me to take it out into the front yard and dismantle it by whatever means necessary so it could more easily be disposed of. It was not unlike a parent asking a son to go find a tree branch for them to beat him with (this never happened to me, but one hears stories) - I think I might have preferred that, in fact. I kept the little brass MOTOROLA HI FI plate you see there in the upper left of the grill cloth.