I would be very surprised if most countries required this. The justification of minimum wage is to keep the risk-takers from shoving all that risk onto the lowest level of employee. The employee is then given a min. wage and the risk taker may or may not take anything home at the end of the month.
I suppose one "benefit" of such a requirement is that a lawyer could no longer take on worthy projects for free ;-)
I believe most EU countries require you to pay the social/health insurance on a "virtual salary" (usually tied to minimal wage or similar.) This is to curb evasion of the social security payments by setting up "businesses" whose sole purpose is to provide labour to a single employer.
In the Nordic countries, at least, that only applies under pretty specific circumstances (which try to target the tax-evading cases you mentioned). In a normal case, if you're self-employed, you pay social contributions only on what you actually make, which might be considerably less than minimum wage if your business is not very successful. Actually have a friend who recently filed taxes in that circumstance, since his one-man mobile-game studio didn't sell very many games in 2012.
I suppose one "benefit" of such a requirement is that a lawyer could no longer take on worthy projects for free ;-)