At the end of the day.. you will have ZERO-0.2 sec of a delay between actually clicking a button and entering a menu, it will be no big deal at all. (PS5 SSD)
GT4 had issues with the speed of menus loading more than the awesome City map screen. I think Kaz only allowed this style of menu because it's negligible in light of the PS5 SSD and load times.
You're missing the point. It's not the delay in clicking a button that makes it bad design. It's the unnecessary time spent finding what you're looking for and getting the cursor to it. You can have an internet link that loads instantly, but if you have to scroll through 4 pages of cat gifs to get to it every time you're not going to consider that a good UI experience even if you really like cats.
Because you're involved in the experience. It's the character of the game we can learned to love. You're not just cycling through a menu, you're looking for your destination.
Which would be fine, and it is good for a game and it's menus to have some unique character. But that character shouldn't impede usability. I'd go so far as to suggest that it's completely possible to make a city map styled menu like this that is far more intuitive and usable, probably to the point that it would be equivalent to any other modern UI for practical purposes.
For starters, have all the available options on a single screen so that people who are unfamiliar or who haven't memorised the placement of every item aren't scrolling from side to side hunting for stuff.
Maybe some groupings of similar or related items, either by having them physically close or by using the background city to delineate them.
Clear placement such that using the Dpad is both possible and has predictable outcomes.
Some shortcuts, probably as combinations of shoulder and face buttons so that advanced users can quickly get what they want without even having to navigate the menu.
I'm sure there's heaps more than this, I'm no UI professional or anything.
It's not super hard and it doesn't have to take away the character of what they're trying to do. It just takes a little thought about minimising the work that people have to put in to navigate the menu. Which should be only a good thing, the menu is something that is supposed to help you on your way to play the game. If it's impeding you from getting to where you want to go, it's not doing it's job.