Since the number of levels in the tree is generally small compared to the number of buffers, this paging scheme will ensure that the root page is always present in memory; and if the root has only 2 or 3 children, the first-level pages will almost surely stay there too. Any pages that might need to be split during an insertion are automatically present in memory when they are needed, because they will be remembered from the immediately preceding search.
"the first-level pages will almost surely stay there too" this is not a serious analysis bro you've been riding people's coattails for way too long!!!!