Having a set of keys to your property - How important?

[Grant D.]

I just closed on a few single family homes out of state that are currently tenant occupied.  I was told by my real estate agent after closing that they previous owner did not have a copy of the keys to the house, as the tenant had always let them in.  I asked my property management company, and they did not seem to think this was an issue.

My question, am I crazy for finding it strange that neither my property manager or I have a set of keys to the house I own?  How important is this?  Is it worth re-keying the houses now...or just wait and do that when current tenants move out?  Any thoughts?