The problem is that you loose all support features by the software by doing it that way. Not even simple design rule checks can be done as the software can not really know if the connection is made on purpose or on accident. (Maybe older software had modes supporting this usecase better. But current PCB design software simply is not build to help here at all!)
If a board is simple enough to be done purely on the pcb side then the schematic can not take more than a few minutes to create. And these few minutes can safe you from a wrongly made pcb. -> Invest minutes in preparation, possibly gain hours or even weeks at a later point. (Weeks because you might need to trigger a new production run. Can take weeks till you have the fixed PCB in your hand.) -> To me it is clear which option i choose.
The schematic has the added benefit of being a good documentation of the system. (assuming the symbol for its components are well made and not just a row of numbered pins. Creating such a symbol only takes a few minutes so worst case double the time expected for creating the schematic. <- Still much less than a mistake can easily cost you!)
Even if there is only one IC on there i bet you that you will not know (without looking at the datasheet) which pin does what if i ask you in a year. (For most designers i would be willing to reduce the time to a few weeks. Especially if they have more than one project running at the same time.) A schematic simply makes maintenance, sharing, quality control, rework, debugging … much easier. (I would even argue that some of these tasks are to be considered impossible without schematic.)