As much as "impartial" as an idea random choices are, the speed of picking is in the GMs capabilities/experience. The ones hosting LTS should be experienced GMs in PvP, and that's the best bet to be "fair" and quicker in the side-picking phase.
There will always be a time when Lady Luck puts everyone better than the other one to one side, and the less-good PvPers in the other. However if it's at the current system, and the GM knows his/her way around PvP and the PvP scene, it'd be easy enough to decide what to pick over who. There will not be always an equal ratio of classes to be split, and the Dice system will take even a longer time to match who should be paired with who to do a /dice, rather than if it's based on what PvP revolves around.
Also it's not a nice thing to say that LTS isn't for the new players (half of them do have the chance to win some tokens) and geared people are always picked first. But if it is the other way around, it will work against them, seeing that to actually win, these "pros" will have to be picked first to carry the newer ones, or lead them to do something better (i.e. not get Devoted just to get one-shot, not cast Angelus, etc.) You can't say they're always useful, and even picking newbies is a hard thing to do. You'll never know who will cause disaster to your team. But they should learn their place and understand as to why.
If you're new and you're just gonna get mauled anyway, just hope that the team you're in will have a use for you in the beginning and cooperate and help them win.