We had representatives of the Scottish Parliament here, and they have a system like that. They only meet three days a week, and bills never take more than two days. They have a business committee.
They make the decision on the program or the time allocation of every bill. They said they couldn't remember a time when they had to have a vote. In that committee, it is always consensus, unanimous, on how long each bill would take. Those were all members of Parliament representing the party, probably House leaders or something, so it's not like if you were suggesting that it's going to some bunch of bureaucrats.