I don't think we need to change the current system in any way.
It would be unfair to newbies and those who voluntarily doesn't want to register to prevent them from picking the most important role in the gamemode. Besides, this way favours well to the "natural evolutions" of the presidents: a newbie, who decided to shoot his securities at the spawn and who died a minute after, would likely decide to choose another tactics next time he picks presi, and eventually he'd evolve into something better.
As for the ping part... Ping surges are too common even with those who normally has a stable connection, so I also think we shouldn't restrict that. In the end, confused and mindless presidents are not too much of a problem; they are getting killed and substited with better ones, bugged ones are quickly dealt with by staff members. The bigger problem is the lack of presidents sometimes; this suggestion would only worsen it. -1.