Maybe you should look a dog bath sinks or some kind of free standing one. I have actually never had a laundry sink and now with the new washers I really don’t need one all the choices of cycles with the new washer really negates the need for a alaundry sink for me at least.

Many utility sinks are synthetics, deep. and utilitarian and not nice looking. Are you looking for traditional porcelain over cast iron, stainless steel, or synthetic? Budget range?

https://www.us.kohler.com/us/browse/kitchen-utility-sinks/_/N-25bb

If budget allows - Kohler's "River Falls" sink is 15 inches deep, you supply the cabinet.

We have a Kohler cast iron utility sink in an IKEA cabinet. We recently moved our laundry room to another part of the house and we re-used the sink. It has held up beautifully over the years. Sons baseball pants crusted with mud were always rinsed and soaked before going into the washer. I couldn't do without it. It is great to have the extra depth when you need it.

I will not go custom

What do you mean by 'custom'? As in a custom made sink? Or custom made cabinet? Or custom made countertop?

Sink deeper than 10" but how much deeper?

DIY?

I quickly found a 12 inch basin depth at Home Depot on US site and a 14 inch on the Cdn. site. Found others as well at higher prices on other sites, so they are out there

https://www.homedepot.com/p/Glacier-Bay-All-in-One-27-in-W-x-34-in-H-x-22-in-D-Composite-Laundry-Sink-with-Faucet-and-Storage-Cabinet-BC2732COM-WH/203678161?epik=dj0yJnU9YzdONHlmUG5HZEVCcFQwQm1ON3V2RUlRUUVYYm9zWUImcD0wJm49R3NyMUhjVFVsYlRfZDN6cmEweWlVdyZ0PUFBQUFBR0JDUlZF