I think players have more investment with a character they start at level 1 (even if they go through a rapid advancement and are level 3 after only a few sessions). For D&D to work as a game where you are truly invested in the character you are playing, death must have some meaning too. I've played in games where a player loses a character and since the rule is you can come back at the same level you died, the player made an exact copy of his previous character and declared it was his long lost twin. This player was NOT invested in his character, but wanted to play a certain class in a tactical combat game with some out-of-combat trappings. In my eyes, while D&D can be that game, it can also be a different kind of game.
In a game where everyone begins play at 1st level, new players start at 1st level, and characters that die must be raised or you begin a new one at 1st level, death is a very real element of the game and I'd wager you'd need a specific group of people (including a skilled DM) to play that game. While it's true mechanically you can contribute very little to a 12th level party at 1st level, there are still many ways a character can impact a story (even a combat) that are not level-based.
Here's some tables of starting points for 1st level characters that are joining higher level parties:
Party is 3 levels higher:
1: Wealthy - you start with starting gold multiplied by 200
2: Connected - you start with a roster of NPCs (up to 10) who owe you small favors or are already on good terms with you
3: Trinket - pick a magical weapon or armor to start with
4: Snake Eyes - you always re-roll 2s
5: Catalyst - you are an important element in an upcoming plot which the party must protect. Pick a level 1 spell, you can use it 1/day.
6: Pick 1-5 or roll on the 4-6 table
Party is 4-6 levels higher:
1: Rich Nobility - you are part of the nobility for a major region and part of the highest social caste. You can call in favors from a variety of people and start with a credit up to 20,000 gold.
2: Magical Birthright - pick an 8th level magic item to start with - the item only works for you.
3: Leader - you start with a band of followers (up to 30) and a base of operations with enough resources for it to operate for two more months.
4: Prophet - you can see elements of the future and they always come true unless you personally change them. You are immune to illusions.
5: Genius - pick a skill, you only fail if you roll a 1. It is automatically favored for you and if it involves creating something the quality is noticeable (you could one day paint the Mona Lisa or sculpt the David).
6: Pick 1-5 or roll on the 7-10 table
Party is 7-10 levels higher:
1: Artifact - you start with an artifact, which operates but is not complete (it will either stop working or is not at full power).
2: Inhuman - you somehow are unnatural; you either contracted vampirism, lycanthropy, or are the progeny of a magical being (dragon, celestial, etc).
3: Wistful - you start with a Ring of Wishes with 3 charges and a treasure map.
4: Saint - you have been declared a Saint by a major religion and your god watches over you. Your faith has outfitted you as if you were a 10th level character (items the last Saint wore).
5: Lapsed Hero - you were a famous hero once and start with 8th level gear, but have not adventured in 20 years. Your inactivity combined with a nefarious spell has led to your present lack of skills. If you can break the spell you gain 3 levels immediately.
6: Pick 1-5 or roll on the 11+ table
Party is 11+ levels higher:
1-2: Heir - you are the son/daughter of a prominent member of the ruling social structure with all the associated benefits (and dangers).
3-4: Superman - your three lowest stats are changed to 18, 17, 16 and pick an element. Unless that element is present you do not die, but you can be knocked unconscious (negative damage stacks up to -100, but heals regularly). Your heritage is alien to the world.
5-6: Prodigal Learner - you gain triple experience until level 10 and double experience until level 20. Also pick a stat to change to 19. You never have multiclass penalties and all skills are favored. Your heritage has some fame (or infamy) associated with it.
If you would roll on a higher level table you can always pick something from a lower table (so if the party is 11+ levels higher you can select anything from the other tables) and the DM can improve it at their own discretion.
I'm not trying to say that these starts entirely make up for being level 1, but the game is supposed to be fun. Some of this stuff is hard to incorporate into a story, so its obviously up to the DM, but I tried to think of things that would make for a more memorable story/experience and not necessarily infringe on the regular party and its goals (though admittedly some of the higher tables do).
Personally I wouldn't want to start a game with character that were more than 10 levels higher than me unless my character would be important to the campaign in some way.