Here's my argument against making new characters start at 1st level when the party is higher level.
I just played a D&D 4e game where my 1st level sorcerer (ranged striker) was constantly overshadowed or pushed aside by the 3rd and 4th level characters. It was not fun.
In combat, I could plink away at the monsters, but I wasn't nearly as effective as the rest of the party. The encounters were geared more for a 3rd level party, so at every turn I feared that one hit would kill me.
In skill challenges, I felt like I shouldn't even participate. Other characters could do almost everything I could do, and better. If I failed a roll, I risked setting us back.
Since this particular campaign was a Western Marches style of game, the character roster changed from session to session. I felt like my spot at the table would have been better filled by someone with a higher level character. I feared that other players felt the same way -- perhaps an irrational and unfounded fear, but I felt it.
The justification for starting every character at 1st is often phrased as "make them earn the levels." In a game where the DM tests the mettle of the players and a lot of characters die, survival is a badge of honor. Sometimes the feeling is that lethality is so high that no one is going to get so far beyond 1st level anyway. None of that changes the fact that I felt useless and overshadowed playing my measly 1st level sorcerer.
If you still insist on starting new characters at 1st level, consider giving them some magic items that are more appropriate to the other, higher level characters in the party. Say your party is all around 4th or 5th level (with magic items ranging from around 4th to 8th level), and your character dies. You create a new 1st level character, but start with some magic items in the 4th to 8th level range. That might help take the sting out of starting well below the average party level, and your character's effectiveness will eventually outstrip those magic items.