The Minimum Wage has worked out pretty well in the UK.
Btw, we British at least try to maintain the appearance of sensibility & wisdom so there is a quasi attempt to address my concerns from the OP with a different minimum wage for those under 18 and a government push for apprenticeships/trades.
That said, it still temporary band aids that doesn't do much of anything. Its also worth noting, the highest minimum wage here is just about $15 and thats in London.