When you do a sport, like tennis, boxing, or whtever else -- what you've done in your training is teaching your stem brain to react and coordinate doszens of simultaneous tasks.
True... but only up to a point.
Each of the "automatic" background tasks you're performing does consume a bit of your overall capacity. Professions that have to deal with this explicitly because failing to manage it is dangerous call it "task loading". Take two examples: basic, automatic skills of divers and pilots.
Managing buoyancy is a skill that requires considerable practice for most novice divers. You have to regulate your breathing to maintain an average lung volume that keeps you at neutral buoyancy, not rising or falling (much) in the water column, but your breathing also has to be sufficient to supply your body's needs, and you also have to notice when your situation is changing so that you can't regulate with lung volume alone and then adjust the amount of air in your buoyancy compensation device (BCD).
New divers often find buoyancy difficult even with full attention. But with practice it becomes first easy, and then fully automatic, even when in the middle of the water column with no ready reference points. I have ~400 logged dives and I no longer even notice it, my perception is that I just "naturally" stay neutral except when I wish to rise or descend, and then it just happens. I find my hands occasionally reaching to adjust my BCD, but I don't think about it.
Pilots similarly have to learn to maintain level flight, using both direct observation out the window and instruments. It's hard and requires full attention for quite a while, but then becomes natural and automatic.
Once these skills are developed, they feel completely automatic, but they're really not, which becomes very apparent when you start piling up multiple "automatic" tasks, and possibly add a non-automatic task on top of them. As you add more "automatic" tasks, their quality degrades, and when you throw in a non-automatic task you find that both the automatic tasks are executed poorly and the non-automatic task is more difficult.
For divers, this becomes really apparent when, having mastered buoyancy, they begin trying to do other things like executing search patterns, or building or welding something, etc. Even something as simple as looking at a compass to determine heading while navigating can result in divers suddenly discovering that their "automatic" buoyancy control has disappeared and they are rising or sinking (usually rising). To some degree this can be mitigated with more practice/experience of the "automatic" skills, but it never goes away. One solution when performance of a complex skill is required (e.g. welding) is to eliminate buoyancy control as a requirement, for example by going to the bottom and adjusting the BCD so the diver is strongly negative and can't float up even with lungs filled to maximum.
Pilots address the problem by defining a strict hierarchy to three important automatic or semi-automatic skills. The phrase is "aviate, navigate, communicate", and the idea is that when task loading begins to overwhelm the pilot they focus entirely on flying the plane first, and only when they are confident they have that fully under control do they pay attention to course and heading, and only when that is fully under control do they pay attention to the radio. Of course, when not overloaded they do all three things at once, all the time, and don't really think about any of them, free to watch the scenery or whatever. But the automatic skills break under load, and when they break the pilot has to consciously "take over", and to prioritize conscious focus on the right tasks first.
Driving is another good example. It feels completely automatic... but I know firsthand that it's not. One way I know this is by what happens when I listen to audiobooks. I cannot listen to a book unless I'm doing something else. The stream of information isn't sufficiently dense to occupy my mind, so my mind wanders and then I suddenly realize that I haven't heard the last five minutes. But when I'm driving, that doesn't happen. It's clear that although driving feels automatic it does consume enough of my attention that I no longer have enough excess capacity to begin daydreaming. Driving + (good) book is close to my limit. I also find that doing non-word puzzles (e.g. Sudoku) is enough to keep my mind from wandering away from a book. Word puzzles don't work because I can't do two language-oriented tasks at the same time (some people can).
Anyway, the point is that (a) I hope there's more to this research than appears in the summary because it really does seem like it's well-understood and (b) background tasks feel completely automatic, but they're not. They still consume attention, just less, and subconciously.