I don't agree with it, but I don't at all think it's mad.

Typical profit margins at companies are under 10%. To me it seems perfectly plausible that changing the incentive structure around how a company is operated would have a way bigger impact than that. (There's also executive pay which is higher in private companies, but is typically chump change compared to profit).

So you've got to put yourself in the shoes of someone who fervently believes that there is a lot of waste in the public sector. That is, despite decades of effort at trying to reduce or eliminate it. And, let's get one thing out in the open: there is a lot of waste in the public sector. (It just so happens that there is also a lot of waste in the private sector, and generally less waste in the public sector than its detractors say) So if you believe that, chucking 10% profit at shareholders - who in the case of the big, trumpeted privatisations of the Thatcher years - were supposed to be ordinary citizens as shares in British Gas were heavily advertised to the public, and many bought them - seems like a potentially great deal. Not madness at all.

This was part of a major rethink not so much about "how to run individual public services" but "what is the role of the state, and what is it best placed to do?" It was felt that we'd already looked into why public services were running badly, and got to the end of the road.

not let some rich people become richer off of it.

And just to emphasise, the idea of privatisation was not "let some rich people become richer." It was to sell shares in privatised companies to as many people as possible, and make investors out of all of us. In one way, it worked: millions of people bought shares in British Gas. But it didn't end up sticking: most people who bought shares later sold them, making some decent money but yielding the longer-term benefits to bigger investors.