The child who asks for company is not always asking you to provide entertainment.

Come and play often means stay near me. The request is for presence rather than performance, and adults frequently answer it by organising an activity, which is more work than what was wanted and slightly beside the point. A child building something on the floor while you read in the same room is being given exactly what they asked for. The nearness is the content.

Try saying yes without a plan. Sit down, keep your hands free, and let them lead or not lead. Fifteen unhurried minutes of being nearby usually settles a child more than an hour of arranged fun.