While no one is suggesting that Google is "responsible," my intention is to open a discussion on the potential regulation of search algorithms. Unfortunately, this has turned into a critique and questioning of my business practices, which are not subjects for debate.
What is your point though, it seems to be search engines should be regulated, and publish their code/algorithm, but what for, how and why?
I firmly believe they should be subject to regulation, and they are, FCA regulations, the right to be forgotten etc. Should they have to publish their code so others can copy it? No, plus, I'm not sure it would help you even if they did.
When the Yandex search leak happened last year, there were 17,854 ranking factors in their code, this is simpler than Google's and didn't make use of Ai anywhere near as much. The web has well over 1 billion websites, should Google index them all, and in what order? Many millions of which are old, rubbish and never updated... others attempting to game the search engine. Any attempt to regulate this in the way you suggest would be a nightmare, and inevitably make things worse.
Should one search engine be able to have 85%+ of the search and digital marketing landscape? No, but there are laws and regulations in place to stop this now. Hence why the monopoly route is the best, Google is probably too big, buys too many smaller competitors, and leverages loads of dominant market positions to further its domination, that is what needs a detailed review.
The reason people are referring to you and your situation with Ai SEO, is that is where your issue lies. However, I'm not sure SEO regulation is any sort of panacea; building work is regulated, car sales and garages are regulated, you still get rogue builders, dodgy garages and unroadworthy cars being sold all the time.
You should have had a schedule of work as part of your outsourced SEO, and had targets for work/improvements, and what the short and long term goals of the changes are. We do this sort of work and offer these sort of guarantees for SEO and PPC, we don't get clients websites deindexed.
Put your website back how it was before it got deindexed, don't pay your SEO company. Then engage someone who can improve the performance of your site, rather than trying to battle a corporate behemoth, via the UK government, who won't be interested.