What does child labour and slavery being profitable have to do with whether “without regulations we’d still have child labour” is a compelling argument?

At the micro level it may sound like good economics. Slavery is not good macro economics. For example, slaves in the US south were intelligent human beings that had they been in the free market with their ideas and efficient use of time and labor, the south would have advanced beyond plantations at a similar rate to the north prior to the US civil war.

Even if it turned out that slavery was enormously profitable at both micro and macro scales that still wouldn't make it a good idea. Just because something is profitable that doesn't mean anyone should involve themselves in it, all it means is that someone is going to be more likely to try involving themselves in it. It falls on the rest of us (and so our governments) to punish anyone who acts in ways that are both abhorrent and highly profitable and that punishment must be much more extreme than any potential gains for it to work as a deterrent.

We should tell this to Dubai's migrant workers.