I do sometimes call myself a single parent but perhaps it’s more accurate to say resident parent or main carer. I am lucky that my ex pays, but he doesn’t regularly have dcs. And as my dcs are getting older I find it’s easier for me when he doesn’t have them, because meal planning, clothes, social events, uniforms, homework, all routine gets disrupted when he has them, and when they come back it takes a day to adjust to each other again. They sort of transfer allegiance at each move and become slightly less close - hard to explain!
As the main carer all the appointments, uniform shopping, clothes and shoe shopping, emergency leave, play dates and parties, holidays, washing and ironing, school trips, parents evenings, dress up days, school projects etc are down to me. He doesn’t have to do anything, although when he does everyone knows about it 
I ALWAYS have to put the kids first and am the default if they are ill or he cancels last minute, he always has the choice.
Every situation is different and people are quick to make assumptions