A parent, never has to be playing with/entertaining their child *constantly.*
A child, also has to learn, their OWN cues and to have curiosity and imagination etc.
It also ENABLES a child, to learn the routines/rhythms of a home and what their Mom does and needs to do. ie: cleaning and chores. It is NORMAL stuff... not anything to feel guilty about just because you have to do it. Thus, if a child is ABLE to learn these things then it enables them... to also learn how to do it too, when they are old enough or able enough. At that age of 3 for example, my kids liked to "help" me clean. Help... in a fun way. Not as a "job." Just to clarify.
Children, LEARN by playing:
By thinking of things on their own. By also playing by themselves, by learning to "wait" a few seconds when they call for Mommy when she is finishing up with the dishes, by learning that they can problem-solve and think of fun things too, by learning to gauge their own interests and ideas, by showing us what they like or not, by discovering things, and... by learning their own cues.
For example: when or if my son, WANTS TO play by himself instead of having me or his sister always interrupting him.. he will SAY "I want to play by myself for now..." or if I am busy with chores he will say "Mommy, when you are finished with the dishes, can you play with me?" And I say Yes. He does not demand my every waking moment. He says what he needs or wants. He can be patient. In the meantime, he is playing with his cars on the rug. It is all quite productive. And he has also learned roles in the home and how to take turns and how to request things and how to speak up for what he wants. Lots of things, a child learns, just by doing what is normal in a home.
But, if a child is constantly entertained and never left "alone" they learn that they cannot be or cannot be by themselves or are not used to thinking on their own.
Anyway, to answer your question, no.. I don't feel guilty just letting my children be.