Firstly, let's just quash at least one aspect of this thread: Bercow's opinion means nothing if the House of Commons votes *for* something he personally opposes. The Speaker's job is to give the House a chance to express its will. That is all Bercow has done, and all he can do. Clearly he's opposed to Brexit. So what? A Speaker that was pro-Brexit wouldn't be able to force his ideology on the House either. Bercow is just a Brexit supporters' scapegoat for the more material point, which is that this Parliament has rejected, and will continue to reject, either of the two forms of Brexit currently on offer.
With that in mind, is No Deal really the default? I should have thought that the lessons of March 29th and April 23rd would have shown that as long as Parliament has any say, which is always, then No Deal will not happen. The House will not allow it. So even if it were the legal default, then any PM who tries to sit on their hands and force a No Deal exit will be overruled by the House -- in its present make-up at least -- and be forced to either seek an extension or to unilaterally revoke notification.
Moreover, I am not sure that Article 50 even allows a No Deal exit, at least not one that happens "by accident", either. The key phrase, in Article 50(1), is that any member state may only leave the EU "in accordance with its constitutional requirements". If a PM attempted to ignore the House and seek a No Deal exit then that would, I feel, be unconstitutional.
We're definitely getting into a legal minefield here, and I might be speaking out of my backside, but my, admittedly amateur, opinion is that a No Deal exit can only be constitutional if the UK Parliament explicitly agrees to it by passing the necessary primary legislation, and I am not sure that either the EU (Notification of Withdrawal) Act 2017 or the EU (Withdrawal) Act 2018 do the job on their own.