Anytime your reasoning is "we shouldn't do it because it will make them attractive to other companies" you're probably wrong.
You want a company full of super-stars that everyone wants to poach. Otherwise you're just like the companies that prohibit employees from have linkedin profiles or don't give employees training because that makes them more poachable. Crazy.
I'm not saying you shouldn't have employees that are so good others want to poach them.
I'm saying that by giving someone a title (that they might not deserve) you are possibly making them more attractive and more likely to be poached. This was said simply to counter the parent point that "there is no cost".
Let's say I allow you to put on your card "VP of Software Engineering" vs. just "Software Engineer" as only one example. (Forget legalities I am using this to prove a point).
Or, "National Marketing Manager" instead of "Marketing Manager".
Or it makes them less likely to be poached, because potential poachers will discover they don't measure up to expectations after a phone screening. At this point we're all pretty used to sussing out title inflation at step 1.
Or maybe someone will perceive it in a completely different way. At an individual level, big moments in people's lives (like changing jobs) are shaped by the edge cases that lead to actions, not macro average behavior.
Making personnel decisions based on worst case hypotheticals only seems to increase the chance your employees will have a hard time imagining long term career growth by sticking with you. Deflating titles seems about as viable as forbidding conferences. Except where titles impact compensation, all of this is completely independent of actual competence.
You want a company full of super-stars that everyone wants to poach. Otherwise you're just like the companies that prohibit employees from have linkedin profiles or don't give employees training because that makes them more poachable. Crazy.