The idea of auctioning off internships is disgusting. I fully support it being made illegal. It was a dark day for the Tory party when they did it at their Black & White ball. I can't think of a worse way to entrench privilege.
What should definitely not be illegal though is basic work shadowing/work experience. Companies don't have to offer it at all - if it becomes too expensive and over-regulated, they just won't bother. Why would I bother paying a spotty teenager minimum wage to follow me around all day, asking stupid questions? I do it at the moment as a civic duty - but it is a pain. It's already a chore - if it actually starts costing me money as well as time, sorry, but no way.
In my experience, successful meritocratic companies don't recruit based on who you know anyway - though obviously the world of politics is very different.
At an old company I worked for, a personal recommendation from an existing employee guaranteed that a candidate (at any level) would be interviewed - ie, it meant they automatically got through the CV screening, a process in which about 50% of candidates were rejected - but the interviews were just as rigorous as for any other candidate. Indeed, subconsciously , we probably set the bar higher.
The real bar to education is that state schools are - by and large - crap. The free schools, academies, and destruction of the teaching unions will improve them. Education is the one area of government policy which I endorse wholeheartedly.