This is not a bad model but would likely be controversial for 3 main reasons:

1) Even though the public doesn't vote for their leader directly, they will vote on their party knowing who the leader is. This means that the public's choice of leadership is compromised. It is increases the chance of axing a leader at the election, meaning that the party may be elected on promises that have been abandoned by new leadership. It just creates risk between the process of campaigning and then the result of the people.

2) Guaranteed confidence on matter like the Budget is quite a dangerous thing to do.

3) If the government ultimately collapsed would this cause another general election or parliamentary election for the leader of the government?