Increasing the tax rate isn't what matters; the structure needs reform. For example getting rid of income tax and replacing it with revenue taxes, which are more difficult to circumvent.
You can set a fee of 3% for restaurants let's say, and 10% for some other business (example)
This makes sense for small business
Even if it does mean less restaurants and less eating out, there is nothing inherently more unfair about it.
You can also see for example the digital services tax introduced by France because VAT was not proving effective.
Unless your thought is that businesses would charge more if there was no sales tax. I don't really buy that, though; businesses list pre-tax prices specifically to avoid sticker shock.