The main reason this is such a bad idea is the possibility that a subordinate record that was once associated with a now deleted ID will be associated with a new master record that it shouldn't be. Here's a hypothetical:
master table:
ID | name
1 | john smith
2 | joan smith
allergies
ID | allergy
1 | NONE
2 | penicillian
Now, the table gets updated, John Smith is removed from the system, and a new person is added, but the old 1|NONE entry gets left behind:
master table:
ID | name
1 | joe smith
2 | joan smith
allergies
ID | allergy
1 | NONE
2 | penicillian
1 | tylenol
And the computer winds up going with just the first record in allergies, NONE, joe smith gets tylenol, and dies.
This kind of stuff can and does happen when you reuse master keys. Usually it's less life threatening, of course, like someone getting a Best of Sonny and Cher CD along with their order for Nellie Mckay, but who knows, that could prove fatal for a certain small percentage of the population as well :-)