Just to be clear, a 15 minute city is just an area where the amenities of a city are reachable within a short walk, which is typically a fairly dense mixed use walkable neighborhood. It doesn't mean a whole city where everyone can access everything within 15 minutes, no matter how low-density the neighborhood.
It is funded the same way as everything else in the city. In fact, these areas are often way more economically productive, because you need less infrastructure to cover more people, and the areas have a lot of economic activity. It is usually the economically productive areas of a city that funds the roads and infrastructure to less economically active areas such as car dependent suburbs.
I don't really see why being able to find a workplace close to your home would damage your job security. People choose to work wherever they want, but having the option to not spend a lot of time commuting is nice.
I also don't see why it would be bad for diversity. These kinds of neighbourhoods usually have a lot of different sizes and qualities of apartments, so you get people from all different economic backgrounds living fairly close. There's nothing about 15 minute cities that prevent people from moving where they want.
And I really don't see how being able to walk to the things you need would prevent your upwards mobility. Feel free to clarify this.
I for one live in a European city. I can reach multiple grocery stores, gyms, shopping, cafes, restaurants and parks less than 15 minutes from my home. I'm a consultant, so I switch jobs often, but I usually walk or cycle less than 15 minutes for my commute. The area I live in is also way more diverse than the suburb I grew up in because there is a lot of different appartments in different price ranges, and it is an attractive area for most people regardless of background. There's also public transit close by for those that need to travel further, and there is even a nightly bus service that goes all night. These kinds of areas are also some of the most attractive areas to live in the country, judging by the demand for apartments in the area.
It didn't need special funding to become like this, it is just a matter of the invisible hand doing its job when the policy allows these kinds of neighbourhoods to be built.
However, these kinds of areas are literally illegal to build in some parts of the world (e.g. a lot of the United States), due to zoning laws.