Let her pay for her own insurance. It costs over a thousand pounds for the year and she does not appreciate it.
Just a wild guess, but I'm thinking that the reason an 18yo hasn't instantly stumped up the money herself is not because she's been out regularly blowing a grand on wine, men and song.
Why is it a sign of not appreciating somebody's gift to you, just because you don't constantly tug your forelock and consider yourself their possession/slave?
They've bought her insurance: not her.
The parents can insist as much as they like that they're concerned about her safety or 'just want to make sure she's not doing anything foolish', but if they're totally honest, there's absolutely no genuine need or reason for them to do so - they are only doing it because they can and they hold the trump card over her of being financially-settled middle-aged adults rather than a very young person who has recently entered adulthood and is just starting to make her own way towards financial independence.
As I said before, this will likely change over the next few decades with them exchanging positions of financial wellbeing and independence. If that happens, I trust they won't object to their daughter demanding intrusive and personal details of every aspect of their lives.
The main lesson that we all need to learn is that having money makes you an important person with all of the rights, respect and dignity; and if you dare not to have plenty of money of your own, without any outside assistance, you simply don't matter and should be grateful if somebody gives you a nice warm kennel to live in.
Maybe, once lockdown is eventually lifted, we should make all of the folk who've suddenly lost their livelihoods because of COVID restrictions and are now needing urgent government assistance to keep them solvent stand outside Parliament every evening for the next 12 months and clap and bang saucepans to show their immense gratitude to their financial saviours. Of course, they wouldn't be forced to do this - if they aren't happy with it, they can always magic their replacement incomes up themselves....