Maybe watch a video about the process on Youtube? What you're saying is correct in a very abstract sense, but does not really convey what is actually happening inside the cell. Timing is extremely important because if the proteins worked out of order (which is often different based on signals), wrong DNA would come out. Also, other systems inside and outside the cell have influence on the replication (you don't always replicate the whole DNA, sometimes it's necessary to not finish the whole process and do something else as the last step, etc). And replication is not stable at all, btw, but there is very good error handling. And don't get me started on DNA activation.

Cells literally have a clock pathway.