This seems to be more of a "show" mudroom rather than the real thing.The idea should be for the mud room to give the family space(semi-conditioned at best) to change clothes and remove muddy or snowy boots.
The basement is a good place for this...The m-room's floor is sacrificial, saving the other nicer floors. I have seen several houses with showers in the basement(another good idea).
Build the house on a slope and provide a decent basement entrance.

[modern living room design[(https://www.houzz.com/photos/modern-living-room-ideas-phbr1-bp~t_718~s_2105) by san francisco architect Klopf Architecture

[traditional kitchen design[(https://www.houzz.com/photos/traditional-kitchen-ideas-phbr1-bp~t_709~s_2107) by san francisco general contractor Mueller Nicholls Cabinets and Construction]

[traditional kitchen design[(https://www.houzz.com/photos/traditional-kitchen-ideas-phbr1-bp~t_709~s_2107) by san francisco architect Wm. F. Holland/Architect

[contemporary home design[(https://www.houzz.com/photos/contemporary-home-design-ideas-phbr1-bp~s_2103) by san francisco architect Simpson Design Group Architects

[traditional kitchen design[(https://www.houzz.com/photos/traditional-kitchen-ideas-phbr1-bp~t_709~s_2107) by atlanta interior designer Mary Anne Merfeld - Allied Member ASID

[traditional living room design[(https://www.houzz.com/photos/traditional-living-room-ideas-phbr1-bp~t_718~s_2107)

[hall design[(https://www.houzz.com/photos/hallway-ideas-phbr0-bp~t_743) by san francisco architect Klopf Architecture

[eclectic dining room design[(https://www.houzz.com/photos/eclectic-dining-room-ideas-phbr1-bp~t_722~s_2104) by boston photographer Chris Johnson

[mediterranean entry design[(https://www.houzz.com/photos/mediterranean-entryway-ideas-phbr1-bp~t_741~s_2109) by san francisco architect Tali Hardonag Architect

[contemporary kitchen design[(https://www.houzz.com/photos/contemporary-kitchen-ideas-phbr1-bp~t_709~s_2103) by other metros architect Frederick + Frederick Architects

I see only a little relationship with a mud room and these photos of a wealthy man's home.

What kind of space do you have that you can devote to a mudroom function? Is it already part of your home, or do you envision adding it to your current house? Depending upon your circumstances and the climate where you live, it is a very important place.

My DIL turned the breezeway in her older wood frame house into a combo family entry/mudroom. She put a door from the garage into the breezeway, and added a fine red door for most coming and going of company and deliveries. (The real front door is seldom used.) There is a coat closet, hanging hooks, a highboy for sweaters and mittens, a bench to sit on for removing shoes. Yes, it is a house rule NO SHOES on the wood floors. So everyone, guests included, remove shoes. There is also a wrought iron spiral staircase leading to the media room above the double car garage.
In the space adjoining the mudroom, there is the laundry so wet/dirty clothes can go directly into there. And beyond that, is the main floor bathroom. Oh yes. And there is also another exterior door opening to the back yard where the woodpile is located. So the old breezeway, now totally enclosed, has a door on each wall.

She has three children, ages 6 to 15, girls not boys, who are very active young ladies with lots of friends who visit. The random sized slate tile floors are always clean...but she is a stickler for keeping it all perfect. Their home is in Massachusetts, 25 miles nwest of Boston, so it does have some extreme weather.

Is that sort of what you had in mind?
I might suggest that you find your way over to the KITCHEN forum, because so many homes keep the mudroom close to that these days. Especially if they want a Cadillac sort of house.