I have an almost 4 year old (3 1/2) and you would think that with the zillions of toys he has -- he could play by himself. No.
In my experience, with my 5 & 7 year old, that skill doesn't appear until kindergarten or really 1st grade.
If I set my son up with cars or trains or coloring, he's happy for about 10 min? maybe? I have had the most success with playdoe (at least an hour)......he plays with the playdoe & cutting with scissors (great for the hand muscles & writing development). But I am in the room & he's chattering away which is fine (language development):)
I go nuts sometimes when I am trying to get some work done or just household duties.......and he wants to play. But I realize that I haven't spent enough time with him & moreover, who wouldn't want to play with someone else? We, humans, are social beings!
Of course, you want to develop their ability to entertain themselves, but just like the mom who asks if she should let a 3 month old infant if she should let her baby "cry it out" at night because the baby shouldn't be hungry........you just shake your head. Experience has taught us better.
Now my 7 year old is my "teacher" & her 5 yr. old sister behind her. My 5 1/2 year has JUST started wanting to read in her room & draw, build with legos and basically, have alone time.
So, my 2 cents, 4 years old is still too young to expect that behavior. Of course, there may be some 4 yr. olds who develop this skill early, but in my mommy groups -- i haven't met them. That's why they invented preschool/VPK & other 4 year olds!
Oh, and parking in front of the t.v., of course, is not good - -but you can steal an hour in the a.m. & p.m. to accomplish some things......the leap frog learning videos & other educational videos are great. Also, we are dazzled by superman lately.
my 2 cents
of course, i'll be interested to see what other moms' experiences have been,
p.s. our 3 1/2 year old goes to bed at 7:00-7:30, still a lot of time to get mommy work done