Maybe if they were rich, but computers were bordering on new-car expensive in the 80s, and were indeed a hard sell for most working-class American families. Even something as basic as a Commodore 64 could cost you a few hundred dollars, and that was before the accessories got involved in it -- some of which you needed if you wanted to save programs or run commercial software. Some parents could be swayed by the computer's educational value in teaching things like math, reading, grammar, and geography, hence the glut of edutainment titles available for the early 8-bit machines. But even in the affluent town where I grew up, very few of us kids actually had computers.
The real winners of the home-computer revolution were the ones who knew how to cut costs effectively, companies like Commodore and Sinclair, in order to grow the market -- and the market only really grew once component prices started falling once the 80s were underway.
My family was... a little different. My father, a mechanical engineer, actually had a use for computers in the home: when the force and mechanical advantage calculations on your novel engine design became too complex for programmable calculators, a more powerful desktop computer was just the tool needed. He got me a VIC-20, and later a TI-99/4A, so I would keep my grubby mitts off his expensive Tandy business machine.