Because he is a clever player and wants to go one step at a time. I think he might have learned a thing or two from what happened to Romelu Lukaku. Lukaku choose for the club of his dreams and virtually never can play (now and then 10 minutes when Chelsea are chasing a draw or a win, can't be called decent play time).
This also proves that Spurs are becoming an attractive side for promising players.
That said i have also my doubts.
Is Hazard garantueed a first team place in the current Spurs side? In whose place would he play? Van Der Vaart? Saha? Will he be the next Steven Pienaar, Pavelyuchenko or Darren Bent? All good players but completely ignored by Redknapp.
Beside this, as much as i would welcome this (my favourite player, playing for my favourite club), i don't really believe it. Hazard has two dream clubs: Real Madrid and....Arsenal. Approximately a year and a half ago i bumpted into his father...a bloke with who i played football for a couple of seasons a long time ago and who turned out to be the father of Hazard.
We had a talk and when it transpired that his son was Eden Hazard we talked about his future. At that moment it seemed clear that Eden would go first to Arsenal and then (if he would succeed) to Real Madrid. Now of course we Belgians don't care about those stupid rivalries between English clubs (i'm a Spurs fan, but i admire Arsenal under Wenger).So it could be that Hazard doesn't mind at all, which honestly is the sensible thing to do.