I think those are great ideas as that's what I was also thinking with what I'd change and do with the plans if we were building that plan. I'm not a fan of the only powder room entrance being in the mudroom, l prefer a more formal power room with the access to it in the common areas. So I like your idea of placing it in the butler's pantry area. Now if a plan is large enough to have two powder rooms such a private one also off the mudroom area I like that too. So the family can come in, wash up..... as they come in the door. Love the locker idea and am adding them in our new build as well. I really like what you have come up with. Good luck :)

Your inspiration photos seem to solve your needs. A long bench, with drawer or basket storage below and a double hook (possible a shelf) beneath each window, would give you a lot of storage. You may even have room to add a tall, pull out cabinet at each end or you could modify the closet to have a pull out as well as hanging area. You could add ceiling height, deep cabinets over your washer and dryer and a countertop for folding. If you must have a hamper, as in your pictures, buy a decorative one and store it under your window. After that, just add a rug and it would look great.

It seems that what you really need is a coat closet for storing most of your coats year round. Next priority would be a place to hang WET coats and hats and mittens/gloves while they dry. You need a place for shoes in your mudroom -- perhaps eight pair with four suitable for tall shoes/boots for each of you -- perhaps kept beneath a bench to sit on to remove the shoes and on which books and backpacks could be set until outdoor shoes are changed for indoor shoes or slippers. You could hang a shoe storage bag for indoor shoes or bedroom slippers on the inside of the closet door. You could keep most of your shoes in your bedroom closets. Ditto that with hats and gloves and mittens. Expensive dress coats that might need to be protected from soil on children's play coats that might make it into the closet should be kept in the bedroom closet or in a coat bag if they're to be put in the common coat closet. The mudroom would be for a convenient place for those coats and accessories just used or just about to be used. Focus on the coat closet and storing other accessories to meet immediate need. Then teach your children to take their backpacks and books to their rooms once they've shed their coats and changed their outdoor shoes for indoor shoes or slippers or flip flops. You could use the 57" wall as the back wall of your coat closet. Find the heaviest coat with the widest for the largest person that lives in the home. Put that on a very sturdy hanger and measure how deep your closet needs to be -- how much of the 38.5" wall will be needed for the side of your closet. If you need 24" for your coats and 4" for the wall (with closet door facing garage), then you will have 10" in width and 12" in depth to build in shelving (at least 4 -- one for each of you) for hats and mittens and gloves just used or soon to be used and 2" for hanging your door. You could have a top door behind which you'd have the adult shelves and a bottom door behind which you'd have the children's shelves. You could hang hoods for umbrellas on those two doors. The 36.5" x 27" corner could be for a hall tree or a three foot wide bench with at least one shelf below for the children's shoes and/or dirtiest shoes. The adults could return their cleaner shoes to a fabric hanging shoe shelf in the coat closet. https://www.google.com/search?q=fabric+hanging+shoe+shelves+for+closet&source=lnms&tbm=isch&sa=X&ved=0ahUKEwilg5r_-Y3lAhVuU98KHSFXBUIQ_AUIEigC&biw=1328&bih=617#spf=1570582032538 There could be a mirror and/or hat rack above that bench. Also, along the middle of that 75" wall on the left as you come in from the garage could be hooks for temporarily hanging wet or dirtier coats and accessories. You'll need to leave a couple of feet clear near the kitchen and garage doors but in between that still leaves room for several boards/w/shelves/above on the wall with a few hooks on each -- at least one for each member of the family. In front of the left side of the closet -- left of the closet door, you might add a hat rack for guests to hang their coats and accessories.

You should get a closet company in to make something that fits your space and needs. This is our kid side of the mud room. On the other side we have storage and shelving and large closed cupboards. Also replying station and dog food.