Not a single one of you would go to work unsure if you'll be paid or unsure of how much
You’re ignoring the responses from me and others on this thread who run similar businesses, but take a longer-term view of their businesses than you appear to.
As a self-employed business owner who sells a service to private individuals much like OP, I can tell you that Covid has cost me tens of thousands of pounds in lost revenue and my finances are currently very very tight. We’ve had to put off a house move and seriously tighten our belts. Our future is looking less rosy than it did before.
Every time a client asks me to cancel or reschedule an appointment it costs me money, just like it does you and also the OP’s salon.
It’s painful, especially in current circumstances.
But I also know that for long term financial success I have to be mindful of customer loyalty and my reputation. If a client asks to cancel and reschedule within the cancellation period, I usually do unless the client has already been flaky, despite it impacting my bottom line in the short-term. Obviously, I don’t allow piss-takers to get away with repeated flaking, but a one-off from a loyal customer who otherwise ‘gets it’ would absolutely be accommodated.
This is because I understand the value of having higher revenue over the medium to long-term, rather than a smaller bird in the hand today. The ability to say no to jam today, so that I have more jam tomorrow, if you will.
I would far rather lose £130 today if it means making £4K over the next three years, than insist on taking £130 today, but making no more money in the future. That’s good business sense. Anything else is dumb short-sightedness.
You ask if people would work for free, without seeming to realise that this is the mindset of an employee and that as a business owner/entrepreneur/sole trader you need a totally different mindset to succeed. A short-term employee’s attitude of wanting a weekly pay slip for clocking on won’t serve you well for the future.
You need to invest time and money in a business and that might occasionally mean writing off a payment or working for free. Nothing wrong with that if it ultimately grows, rather than stunts, your business.