If you use a dishwasher and/or have a deep laundry sink, or if you never wash a large amount of fresh veggies, or if you never hand wash and rinse delicates in your kitchen sink, you may not want or need a double sink; however ...

I prefer the deepest double stainless steel sink I can get so that I can put unwashed veggies in the one side and set them in the other side after washing them before peeling them. The repeated rinsing of turnip greens straight from the garden necessary to remove sand is much easier when you can move the greens back and forth between the two basins.

Hand washing dishes is also easier when you can set the washed but not yet rinsed pieces in the second sink basin.

I prefer a faucet with an arc high enough to hand wash a large serving tray or huge boiling pot.

I prefer levers (rather than knobs) for my faucet to control the water so I can turn the water on/off with the back of my hand or wrist if my hands are covered in flour or have meat juices on them;

I also prefer my faucet have a sprayer in order to be better able to rinse not only foods and dishes but also the sides of the sink basins.

Even when I had a dishwasher, sometimes the amount of dishes dirty at any one time -- such as after a lunch including sandwiches or a single spot soup or stew -- was so small that I'd wash them by hand anyway. One dishwasher is more than enough for the average family.