|The original Basic D&D|
1 - It keeps everything together and lessens the chances of someone forgetting their sheet. As GM I keep everything for the current campaign in a single bag so it doesn't get mislaid or left behind.
2 - In between games or campaigns I like to have the sheets to hand so that I can tailor certain parts of the game to certain PC abilities so that everyone gets a shot at the limelight. Having the sheets to hand is a bonus.
3 - I don't like several copies of the same character sheet because they are all set to change as the PC grows. I don't want any 'that's not what it says on mine' arguments, which may sound strange if the player has a copy of the exact same sheet but it has happened.
4 - It minimises the sudden appearance of phantom skills or equipment between sessions. Some of my players over the years have added beneficial stuff to their sheets in the hope that it isn't noticed by the next session.
5 - If any players want to write up info on their PC they can write down their skills and abilities and base it off that. They don't need a copy of the character sheet to make detailed background notes for their character. If a player desperately wants the character sheet for any reason then I have them write it out again/photocopy it for their own use but I have them use the character sheet that I have during the game.
6 - I prefer any upgrading/advancements to be done at the table in front of me and the other players so that everyone is aware of any changes to the PC (that they want made public, at any rate). This way I can keep an eye on any rulebending that might go down.
7 - If the player does not turn up then we have the character sheet to run as an NPC during the absence.
It's not just a question of me not trusting my players (although, over the last 3 decades I have run across some who 'modify' their character between sessions, which is why I started keeping them in the first place). It's also a question of practicality; it's simply easier for me to hang on to the character sheets between sessions so that nothing is forgotten.
Nothing is ever forgotten.