Is it unrealistic to expect from a 6 year old

Is it unrealistic to expect a 6 year old to play by themselves while I read or get house chores done ? My son has an extremely hard time with playing independently. Like even as soon as he wakes up he's mommy play with me please please please and I haven't even started the morning. All day sling he's asking me to play more and more and more it's never enough for him no matter how much I play with him. If I need to do dishes or vacuum or something he goes shuts asking me to play even if we just did and he won't do anything until I'm done. He will walk around sulking. If we go outside to play sometimes I ask him to go play while I watch him and read and he absolutely won't let me read he's in my face the whole time crying for me to play even if we already did. He gets lots of love and attention and it's never enough. I feel like other parents don't have to play all day every day. I talked to his pediatrician and she told me he should have better independent play skills by now but because he's very typical otherwise she doesn't see any problem and told me to just keep trying. My husband tells me it's too much to ask of a 6 year old to play in the yard while I watch him and read.

Any advice and is it too much for me to expect from a 6 year old ?