In the UK:
Every residence I've ever even been in/seen online has the washer (and dryer, if present) in the kitchen, or in a utility room which is as near as possible to the kitchen. I've never seen a 'laundry room'. The closest thing would be a utility room, but that usually has all the laundry stuff, plus tools, dog food, garden implements, basically 'heavy duty' or dirty things that you don't want in the main house.
(Utility rooms also don't always have a sink, and the sink is usually a 'dirty sink', for cleaning things like BBQ grills, I've never seen a special sink for laundry. )
To be honest, I've always thought that Americans make a huge pulaver out of doing a bit of washing. It's always depicted as some massive undertaking, with the need for a special room and all these special steps. (Sorting, washing, opening the lid to add rinse stuff, drying, folding...)
Everybody I know (including people with several young children) just chucks the clothes in the washer, takes them out, dries them, and throws them in the ironing basket until they can be bothered to iron them and hang them up (or if you're me, you just put stuff away when it's dry, I don't iron stuff unless I need to be smart).
The concept of 'laundry day', or needing a 'laundry room' is just silly to me, now that you can chuck it in the washer (which takes two minutes), and hang it out to dry (which takes 5 minutes). Even if I had several kids, I'd struggle to spend more than 20 mins a day on laundry, especially as most kids clothes don't need ironing.
It is a bit offensive to claim that "Americans" make a "huge pulaver" about anything- "America" has so many cultures and subgroups that it isn't possible to say anything much about us as a unified group.
As far as having your washer and dryer in the kitchen, while it may be common for you, where I live isn't done if possible, and would be a sign of poverty, especially because the stereotype of extreme poverty in some areas is that they have a couch and stuffed recliner on the porch and a washer and dryer hooked up in the kitchen (because the laundry alcove or room is being used for a bedroom). Most kitchen don't have the space or hookups available (except for some rentals which add a laundry space or alcove for hookups in the kitchen)
Here in Wisconsin temperatures range from 20 degrees F. to -30 degrees F, with windchills that can drop to -52 degrees F. Hanging clothing outside to dry from November through March or April would range from dangerous to painful for 6 months of the year.
And in order to keep whites white and blacks crisp I do separate clothing. On laundry day I have 2 loads of towels (for 2 people), 8 pairs of jeans, 4 or 5 pairs of pants, and about 14 shirts, plus underwear/socks, and jammies. It takes my husband all day between other things- stain pre-treating and spot removal, 45 minutes for each load to wash, an hour to dry, 20 or 30 minutes to fold/hang-up/put away each load. We're talking about 5 loads or so, so really not just a minute to pop it in and 2 minutes to dry.
I work a professional job- if I don't do laundry well my clothing won't be okay for work.