Padanarm, I'm sure the queen would not dream of saying to her secretary, "Have the invites gone out for my next garden party?" However, there is nothing whatsoever wrong with a bloke telling his mate, "I can't go to the match on Saturday, 'cos I've accepted an invite to my cousin's wedding."
It's not sloppy, it's colloquial.
If command - first recorded as a verb in 1300 - can become a noun in 1591 and be perfectly acceptable thereafter, why can't invite - first recorded as a verb in 1553 - become a noun in 1659? At that point in time, invitation itself was no more than a Johnny-come-lately, having been around for less than fifty years!
A word's part of speech is constantly subject to change. Is key, as an adjective..."Winning hearts and minds is key"...sloppy because it has been around for only a decade or two? The potential such list is virtually endless.
If it's what most of us say - as in mobile for mobile phone, mentioned by SH above - it's OK as far as I'm concerned.
But what the hey!