No, in practice, there's no boost perpetual motion machine. You'll usually just use that boost up and that'll be it.
There interruptions for that perpetual motion machine are pretty simple and common:
You have to roll the dice. You're not just effortlessly always going to succeed with style, or even necessarily succeed. Fairly often you'll get a +1 to defend against a +2 attack, spend your boost to succeed on your defense, and... nothing special happens. (Sometimes you'll even be defending against an attack of +8 or +9, and you'll be spending that boost just to minimise the harm.)
Conflicts involve more than just attack/defend ad infinitum. If you're just doing that, you're ignoring two extremely powerful resources: create advantage, and overcome. Recent conflicts in my group have involved the following:
- Intimidating an enormous sandworm (CA).
- Entangling its mandibles in bolas (CA), trying and failing to wrestle it to the ground and into submission (CA), and it breaking free (Overcome).
- Getting swallowed up by a sandworm (CA). Gulp! Those of us still on the outside shortly afterward worked with them to blow the sandworm up from the inside, destroying a sacred temple in the process. Oops.
- A plant mutant smothering enemies in vines to subdue them (CA).
- Someone punching a giant rock door into rubble (Overcome).
Often the shifts of attack are more valuable, so you'll opt to keep them.
Boosts are also super transient, as Ryan Macklin wrote about:
Once you invoke the boost, it goes away. They go away on their own fairly quickly—usually after the next action when you could use them—so use them as soon as possible!
This also makes them relatively effortless to invalidate. Maybe you put Startled on the thug, but next turn you suddenly have something more urgent to focus on — your teammate's in trouble and you have to run for them to get them out of it! You won't have time to take advantage of that Startled boost before the thug's feeling composed again.
Trading boosts forward leads to narrative progress and fun, anyway.
Even when you're trading one boost for another by using it to get success with style on a roll, you're not just moving a number around: you're trading one narrative advantage for another.
This not only keeps the +2 around because the boost would fade otherwise, it moves the story forward and keeps things fun. Each successive boost gives you new narrative positioning from which to try new actions which wouldn't otherwise be reasonable, potentially leading to increasingly ridiculous (and fun!) advantages.
Sometimes you'll be in a position to trade a free invoke or a fate point for a boost. At times this will be a downgrade, because boosts are more temporary, and fate points are more capable to boot. However, when new narrative positioning would be helpful, the trade-off could be quite worthwhile.
I'll correct something else you said about how boosts are acquired:
So, the attack/defend action in FATE Core has as standard the idea that if either side ever gets a success with style, they have the option of reducing their final result by 1 to gain a boost.
Defending with style gets a boost automatically. Only with attack do you have to reduce the value of your hit by 1 to get the boost. (Our group rarely sees success with style on defend attempts. Usually they'd require an invoke or two, and people won't do that just for the boost.)