Is there a option to completly remove the spotlight search function and have it locked by screen time restrictions?

Is there a option to completly remove the spotlight search function and have it locked by screen time restrictions ? The reason why i ask this is bcos even when you lock down safari browser to only allow specific websites in screen time options it is possible to view pictures of adult movie stars with allmost no clothes on or even without. It was brought to my attention when my son used his spotlight search to look up a song of kendrick lamar and when he typed kendr... the search was full with pictures of a adult movie star called kendra... and i am sure that way you can get pictures of a lott more of them, the spotlight search can also be used to look up how to bypass restrictions and screentime and so on. I know with siri and search you can turn off spotlight that it does not show images but this option should be locked behind screentime. There is otherwise no point in only allowing pre selected websited in screen time if you can just go to spitlight and see half naked women and find optiont to bypass restrictions. Or is there a option in screentime that i overlooked ? Thanks

[Re-Titled by Moderator]