You are probably right if we disregard the 20 years of cap-ex investments Google made into having that infrastructure. In order to in-house this we would probably need to own $500M-$1B worth of infrastructure at the very least (web is vast). Yes then the cost per search would be lower.

Maybe it will sound strange, but I do not think of our goal as optimizing for growth and number of users. It is to optimize for sustainability and quality of product. Often these two incentives are opposite of one another. I see us as a small, boutique, premium search brand. I'd rather have us gain more users by improving the quality than by lowering the price.