Personally, I prefer starting characters at 2nd level. This helps explain any multi-classing the character might want to do. It eases certain concepts in better.
Although apprentice classes can do that, too, of course. But then, they eliminated those from the revised Dungeon Masters Guide, didn't they? Or so I heard. Don't intend on ever picking it up. If they were, though, bad move in my opinion. Even with those, then, technically it has to be a favored class that's apprenticed in. So there's already some muxing about with the rules for, say, an elven fighter/bard as an apprentice level character.
As such, no, no cheating for starting higher than first level characters.
Not to mention that a lot of campaigns never reach particularly high.
With that in mind, there reaches a point where killing orcs, goblins and kobolds becomes tedious and boring. Where you want to swat dragons and demons and tarrasques. Though I often DM myself, I can fully see getting fed up with level one after, say, 4 campaigns that were stopped at level 5 or so, and not wanting to "start over" again. Even if the monsters and setting change, I'd still want to see some of that higher level stuff get used as opposed to just being temptations that were never realized, so to speak.
As it is, I'm rotating three campaigns, two of which started at level one, another at level two, but in two cases, they've both been running for some time, and with the other level one campaign, it was just meant to be a one-shot so I could actually get some use out of my Midnight campaign book, and I didn't particularly feel like making an adventure up, so just used the level-one adventure from the book. The other two games were also levels 5 and 9 or so respectively, anyway, by that point.
In either case...no, higher level starting games are fine. With the exception of the Midnight one-shot that turned into an on-going game, all of my one-shots have started well above 1st level, as a matter of fact.