Zero hours contracts are NOT illegal in most of Europe. They and similar casual contracts are common across the EU although they appear to be most prevalent in the UK and Austria.
It is wildly untrue to say that the vast majority of minimum wage jobs are zero hours. The number appears to be going up but some of that rise is thought to be due to employees being more aware of the nature of their contract.
For some employees the flexibility offered by zero hours contracts is perfect. For others it is unsuitable.
Similarly for some employers where demand fluctuates hugely from day to day it would be next to impossible to run a business without such contracts.
The government should ensure that such contracts are not exploitative, that workers are not pushed into them against their will, that employers are not using them as a way of dodging taxes and so on but a complete ban is not the answer.