Any sale of a search engine to Google is an asset/talent sale, right? They're not going to operate a competing search engine brand (aside from that one they do user testing at) -- they're going to assimilate its technological and biological distinctiveness into their own.

Google has 23 billion a year in revenue, substantially all of it from two products. Operating an internal competitor to Product #1 will not move the needle. Its, quite literally, less likely to make them less money than changing the shade of blue they use.