It makes other employees scared to resign and shows that company doesn't trust their morality.
It is also a bad idea, culturally.
Coming from Europe I'd say that you can do this differently, we do this differently, and all the terrible risks and obvious reasons enumerated in existing answers don't apply. This is because they only exist in your brains and not your world. They are errors in your judgement.
A company in financial sector.
Some employees of IT dept resigned trough the history, who could technically: steal credit card numbers, introduce back doors, install subtle bombs that would fire in future.
And who could with just a little bit of thinking devise how to do it anonymously (I said it already: IT).
They worked 3 full months after resignation.
They didn't particularly like to work these 3 months and stated it plainly, but they were legally obliged to do so.
They didn't even like the company.
The company could have legally walked them out on day 0, but the decision was to keep them.
The bad stuff never happened.
And they fixed some stuff during the time, cleaned some of 'their' mess, did some knowledge transfer.
It was more than one occasion.
Go figure. Employees actually have some morality. They don't go around harming others just because they see no immediate penalty.
I think that after 3 months if they found on a sidewalk a wallet of their CEO, they would return it.
Their managers trust in that morality. And the upper manager knows that they can trust the lower manager's judgement. The owners know they can trust the upper management. A magical chain of trust.
I believe that other answers, maybe because of the immersion, didn't see what is obvious to me. If you (a person) hire yourself a janitor, and interact with him for years, and as he says he would like to resign the next minute you send guards to escort him? Really...? Because your stuff is so precious? Unacceptable risk, huge liability? A minute before it was acceptable, now it's not? Nevermind how long is the list of your stated reasons and justifications, the action brings a clear message about the employer. It shows how employer treats others, how much trust they have with morality, what you could expect of employer's own morality.
If you see a company that experiences this, and want to find the cause you ask a simple question: "what needs to change before this company can keep employees after resignation?"
If you address all the stated reasons one by one, and somehow magically exclude them all (the risk that an employee would reduce staff morale, poach customers, sabotage, etc) I won't expect the situation to change. I expect they would still have been escorted out and I expect the enumeration of reasons would get new entries. So these are not actual cause: they don't influence reality.
If you re-create the trust in human morality, I expect things to change. This is because you nailed the true cause, not just a stated reason.
Now, how it is repaired, is there a recipe to change a mistrusting company, I honestly don't know.