Keep in mind the stadiums are only used for NFL games/events maybe 10-12 times per year. There are many other events held in those stadiums, especially the indoor ones. NFL teams are not in the business of facility management and booking events so it makes a lot more sense for a city or other entity to build and run the stadiums. The NFL teams are the primary and most visible tenant and they seem to get good revenue streams from non-NFL events held there, but ultimately the stadiums likely aren't built without the NFL team in the first place. So they do go hand in hand. It is rare when you have an owner like Robert Kraft who built his own stadium. He must have the structure in place to manage all that. Good for him, but he's unique.
If a city chooses to not invest in those kinds of projects though that's on them. I know Indianapolis has benefitted greatly from having professional teams and the facilities that come with them. Louisville and Indianapolis are very similar cities in geography and size but very different in perception and the amount of ancillary business the sporting events and conventions bring in because of their investment in the facilities. It may not be a hard dollar bottom line difference that's easy to articulate though.