Are you saying that many countries with VAT have exceptions for small businesses? The number of countries without VAT arguably doesn't add up to "many".
(of course, this is not relevant to the discussion at hand about a business in the US)
VAT is not the only tax you pay. In Poland, depending on the kind of business you are running, apart from the value added tax, you are also paying tax on either profits or revenue (depends on what you do, if you do software - revenue tax is preferred because the rate is lower and you have effectively zero costs).
Of course it gets further complicated if your company is a standalone legal entity, but in that case you have a lot more funny scenarios, e.g. you can go to jail for acting against the interest of the company you are the sole owner of.
All countries have an "exception" for cash transactions. However, only within limits; the government investigators can indirectly infer and estimate unreported revenue.
The business itself pays tax on the net, but the individual pulling money out of the business receives income and must pay income tax AND the additional social security tax.
Alternatively, if it's cash only, they receive 100% of the cash and skip all that.
Most would be still profitable if they paid all due taxes. The problem is that, in many of them, it wouldn’t worth the hassle.. long hours, wearing multiple hats to make ends meet, hard to disconnect, etc.
Most small businesses aren’t fed by VC nor expect an exit. Most are just mundane and boring activities where people expect to receive a premium over a regular job. Or that or they close. Tax avoiding, in many cases, seems to be the path to get there.
