Interesting. I wonder to what extent this reasoning was behind executive support of the Chrome project, and whether it was a factor from the onset or something that Google stumbled upon after developing a browser.
I am 100% sure this is the reason Chrome was funded. (I don't doubt Chrome developers' goal was to develop the best web browser in the world, but business case for doing so is different matter.)
Chrome was also an insurance policy. You can't buy away Google being the default search engine in Chrome. Imagine pre-Chrome browser marketshares and imagine the impact the Firefox-Yahoo deal would have had.
(a) At the time Chrome was launched, IE was dominating with ~69% market share:
https://d28wbuch0jlv7v.cloudfront.net/images/infografik/norm...
And, Firefox/Mozzila was topping out at 25% market share! They were basically resting on their laurels! Remember that the SPDY protocol which is the prototype standard for HTTP 2.0, was invented at Google and was the main innovation within Chrome 1.0. If you do a timed google search 2008-2010 for SPDY you will see that the SPDY whitepaper page was Nov 12, 2009 : https://www.chromium.org/spdy/spdy-whitepaper So Chrome was launched to make web browsing faster.
(b) Google Search does not want to be excluded from all browsers. The solution to this problem is to fund your own browser. If IE will dominate Firefox forever and Google was depending on Firefox defaults for much of its search traffic, then Google was virtually FORCED to create its own browser or they could always be limited to 25% (or less) search traffic share.
I think that having a "Browser account" which synchronizes browser bookmarks and settings and history across all instances of Chrome for a given user, is one of the greatest improvements in browsers in the past 5 years, and all other browsers seem to be copying this idea. If google were the evil empire as you imply, it would be suing the pants off these other browsers, but it is not.