Google already has a copy of most of the internet on their servers - they're quite open about this if at tech conferences (although they claim to respect robots.txt).
I completely agree with you that their monopoly dream is bad - their motto "don't be evil" is starting to sound as ironic as the word "democratic" in some countries' names - but many of the advertising and data-sharing practices on the "open" web are also bad (and sometimes illegal under the GDPR).
Not just Google though - Facebook wants it too (going as far as creating their own internet bubble where Facebook is free, the rest isn't), and Apple (with Apple News), and if Microsoft had a more significant internet presence I'm sure they'd be all over it as well. They prefer to dominate the professional world though, also plenty of money to be had.
