I would enjoy being able to search my history for words that show up in the webpage but not the title or url.
I would like Google Chrome to store copies of all webpage's text. There should be a customizable limit to the amount of storage space the history can take up; personally I would like to have it at 100GB, but I suspect 1GB would be enough for most people. As I suspect that Google has good algorithms to search compressed text, compressing the history would be a good idea, though definitely should be optional if the compressed history searching takes notably longer than searching an uncompressed history.
When the history data size reaches the limit, notify the user, suggesting to increase the limit. Notification should have a "Do not notify again" option. If the user does not increase the limit, the minimum amount of oldest entries are removed to make way for each new entry.
The advantages of this method are: this method works for webpages where the user needs to be logged in to see the desired keyword(s); if webpages are deleted or modified, the user will still be able to find what the user needs; multiple versions of the webpage can be stored when visited multiple times; the user does not need to submit their web history to Google.
Have the personal web history on the cloud in the user's Google account. Just the URLs and titles like current would be sufficient, as you could have the Google search engine run a search restricted to the URLs in the web history. The advantage of this method is lower storage space requirement.