I often don't have time to separate laundry. No, that's not quite true, I often don't care enough to separate laundry (LOL) and I have a feeling that I'm not alone in my 'sloth'. Actually, it works out well for me.
I try to wash the shirts and drip-dry things first, in a full load. If there's more room, I just continue to put, put, put until the washer is full. When they're done, I pop the shirts into the dryer and set the timer for 12 minutes. (HALF a Bounce sheet is plenty) While that's drying, I hang all the delicates and drip dry things. I invested in one of those laundry room standing things ($20.00) and it was twenty of the best dollars I've ever invested. The shirts will be a little damp when the timer goes off. I smooth them out, fold the collars down and hang them to finish drying. It's amazing how little ironing is necessary using this method.
This also means that when the second wash is done, I can put the towels, jeans and heavier things into the dryer, set the timer, and go to bed. I don't HAVE to be right there when the dryer beckons. The towels will wait patiently for me. If there's anything in the last load that's wrinkled, I dampen a washcloth and pop that, with the wrinkled items, back into the dryer for a few minutes. Abracadabra...wrinkles gone!