I reach for elasticated shorts on the mornings when I've got too much on to think about a zip or a button, the kind of day where you're getting kids out the door, bending down to find a lost shoe, then straight into a car seat and out again at the other end. A proper waistband with a fastening digs in every time you sit down, and some days you just want to not think about your middle at all. These let me forget about it until I catch sight of myself in a shop window.
They're at their best through the warmer months, for anything that involves sitting on grass, walking somewhere without a fixed endpoint, or standing about at a barbecue holding a plate and a drink and not having a free hand to deal with a waistband that's rolled over on itself. A well made pair has a wide band of proper flat elastic, not the thin ribbed kind that curls into a tight little rope by midday and leaves a mark. The fabric should have enough weight to skim rather than cling, because thin jersey shorts move with every step in a way that reads as cheap even if you paid plenty. Check the inside leg seam too, a flat one won't rub, a bulky overlocked one will, especially if you're walking any distance. I've got a pair with a drawstring through the elastic that lets me loosen them after a big lunch without anyone noticing, which sounds like a small thing until you need it.
Where they let you down is anywhere smart is required. An elasticated waist pulls the whole shape in towards comfortable and soft, and no amount of ironing gives it back the structure a proper tailored short has. If you tuck a fitted top into them you'll see every gather and pucker of the elastic sitting right under it, so they're not the ones for an occasion where you want a clean line through the middle. They also don't love a big bag or a long coat worn open over them, the extra bulk at the waist adds up fast and you end up looking bigger around the middle than you are, which is the opposite of what you want from something meant to be easy.
Keep them away from anything already loose on top. A baggy t-shirt over elasticated shorts loses your shape altogether, so I go fitted up top if the shorts are soft, and save the slouchy tops for the ones with a proper waistband.