When is custom scheduling software justified?
There are plenty of standard scheduling tools. Custom is only justified when your constraints do not fit into them.
The signal
Your scheduler uses the official software plus a spreadsheet, or a board on the wall. That means the real rules are not in the system.
What breaks standard tools
Skills required per task, travel time, varying availability, expiring certifications, and rest rules. Each on its own is manageable; the combination almost never is.
What custom software must do
Propose, not decide. A human scheduler must be able to override, and the system should learn from those exceptions rather than fight them.
Last-minute changes
That is the daily reality, not the exception. A schedule assuming nothing changes does not get used.
Connect it to communication
A schedule change that does not automatically notify the person affected moves the work rather than removing it.