A partial solution for Version 73.0+ (no search suggestions but still get url history) is to change the default search engine, since the omnibox prediction service is no longer toggleable from the "Privacy" settings panel.
Just go to the "Search Engines" panel, and change the default engine to your prefered provider
chrome://settings/searchEngines
If you wish to keep google but without "search suggestions" you may use this:
{google:baseURL}search?q=%s&hl=en
This will suggest from your URL history instead of predicting a search with "useful" images, products, video or news snippets.
1Running Version 74.0.3729.131 (Official Build) (64-bit). That no longer works. There is no "Privacy" section under "advanced settings". There is a "Privacy and Security" section, but it does not have that "Use a prediction service.." option. I want to be able to put in a URL and have it go there. If i wanted to search, I would put the search string into a search field, not the address bar. I think the developers are doing this on purpose, though I don't understand why – Duncan – 2019-05-14T19:00:16.873
Sadly google is treating even "power users" as babies and locking down their features, better is to move to another browser like dissenter or brave. At the very least change the search engine to duckduckgo – nodws – 2019-06-05T15:21:47.300