We may add a toggle for this. The reason it does not automatically open into a chat is because some users do not want to open up their responses into an open-ended experience. They want to fence in the experience to one with more rails.
The way it works now is perfect as you mentioned it is great to keep users fenced to keep the flow and get to an end goal, this simple fencing is what made me like pickaxe right of the bat, yes put the toggle in if users need it, but keep the default as is. I have created and tested 100’s of GPTs and one of the biggest problem was and is forcing the prompt to keep users on track.