On my PvE characters I have to confess that I'm infuriated by being locked out of my account's skill library when I create a new character. I don't have time or the willpower after a year of playing to get a duplicate of skills I've already collected once - it's mindlessly time consuming, expensive, and it's just not fun!
If I only had one PvE character then the problem would be less pronounced, but as it happens I like to re-roll characters quite a lot and run a handful of PvE characters. After a year of playing I've unlocked a lot of skills, and what I'd really like to do for convenience sake is to have access to all of my unlocked skills accross all of my characters, PvE and PvP alike.
As a veteran, I don't want to become bored of the game by re-doing things I've already achieved - it's really soul-destroying for me now. I hate it. If I could replay the game as much as I like with all my achievements in-tow, without being so locked-down, I could have a lot more fun

The bottom line is: I'm suffering burn-out from re-skilling, and it's a real problem.
edit: (I will add additional information below to make sure this idea is water-tight

--- ADDITIONAL ---
My preferred point for a new character to gain access to previously captured skills is after Ascention (or it's equivalent) to prevent abuse at low level. Only ascended L20 characters will benefit.
Skill Hunter: becomes account based, so you can combine the efforts of all of your characters. Effectively you become the Skill Hunter, not an individual character. That means when a new expansion come out you can roll the new classes, capture their elites and be up to date on your title instead of dragging that Chapter 1 character everywhere - unless you want to, in which case you can. Balthazar Faction will offer another route to Skill Hunter; ultimately it's the personal experience that counts, and I will be capping from monsters

Thanks to everyone giving me feedback to fine-tune this idea, keep it up!
