>>a democratic non-profit foundation
> Isn't that what Nominet basically was and here we are?
Nominet was a non-profit, but not a democratic one. Democracy is not "choose your rulers", but "choose your rules". Having a board/parliament is by definition the opposite of government by/for the people. The simple fact the community has to fight against the board is proof of that.
> a minimum barrier to people simply writing a script and registering literally every domain in existence
That's just not true. First, because that was definitely not the argument presented when administrative fees for domain registrations were brought up. Second, because bad actors usually have a lot more resources than good actors... Sure you may stop a random teenager from registering many domains, but random teens is not who i'm afraid of personally. I don't know of a single time where economic barriers have stopped bad actors from engaging in malicious/hurtful activities. Third, because some TLDs are actually already fully free-as-in-free-beer because they're operated as a public service and they are not facing the problems you mention (to my knowledge), if only because their terms and conditions disallow parking spaces.
> Probably also to provide a financial paper trail in case of abuse, illegal activity or other reasons.
Not sure about that either. In most jurisdictions responsibility for illegal content falls on the hosting provider, not the registrar/TLD. In the rare cases that your TLD is going to seize your domain for whatever reason, whether there's a paper trail or not changes very little because the content is effectively taken down as was requested. Whether that's a feature or a bug depends on what kind of stuff is being censored and for what kind of reasons.
Personally, i'd be interested in a more democratic take on domain seizures. I'm pretty sure most people are opposed to wikileaks/scihub having their domains seized, despite what a board may think.
> or other reasons
Yes, to grow a crazy lucrative business out of infinite resources nobody should be competing for. I'm calling that an anti-feature.