Although I don't like the way Google is starting to control too much online, I believe that using the social network and other information to influence search and other services is the future.
Google’s move towards social search could be the most significant change in the way we use the web since the beginning of Google itself. Consider that with this move, Google is actually moving away from their flagship Pagerank algorithm.
Google has already mentioned it wants to hold our online identity and others have speculated that Google wants to be a “reputation engine” (http://rossdawsonblog.com/weblog/archives/2011/08/breaking-g...).
It is not difficult to see that the next step is to make search results dependent on reputation and on the trust friends and +1’d organisations have in particular websites.
Difficulty to establish identity and trust is one of the main shortcomings of the web compared to the real world, especially when doing business. It is much easier to judge character and establish trust in a local face to face relationship than on the web. Locally we can observe others interacting with a person of interest or ask questions to neighbors who are likely to have some knowledge about each other.
I have been interested in algorithmic trust metrics (http://en.wikipedia.org/wiki/Trust_metric) for a while. If I was starting grad school over, I think I might have picked this field for my research. Things like Subjective logic (http://en.wikipedia.org/wiki/Subjective_logic) are similar to the way humans establish trust in real life and search engines could improve their results by using it. There are ways to quantify not only direct relationships but also indirect ones where one can trust an entity because some other trusted party, trusts them. The fact that we are all connected by few degrees of separation (some say at most six) makes this truly powerful.
It is probably too computationally expensive to generate a complete global trust network for each google+ user but a team of smart engineers should be able to cluster users with similar opinions or apply the relevant algorithms greedily. Although it is a computationally difficult problem, Google might just be the company that has enough servers to throw at the problem.
The trust network paradigm isn’t limited to search. When plugged into a global trust engine, people or organisations that do transactions online, on eBay for example, could forgo the need to rely on vast amounts of random customer feedback to establish trust but instead users could request to see a trust path from themselves to a target person before doing business. This means that new eBay users could bring their reputation from elsewhere with them when just starting to sell. Inversely, it may become possible for google+ users to "+1" eBay’s reputation system and their search results would then contain things that people with good reputation on eBay have +1’d or linked to.
The transition from rankings based on random websites’ link contents which often include SEO manipulations to rankings based on individually chosen trusted sources has the potential to be revolutionary. I can’t wait for the day when each search result is accompanied by text stating “recommended this because you +1’d this guy who +1’d this organisation who links a lot to this site.” The mechanism could be used in every kind of relationships and might help picking new employees, friends, doctors or even politicians.
I hope Google doesn't become a monopoly in this, like many people I am unconformable with their growing reach. However, if they manage to provide a transparent trust network and provide better search results based on it, it will add a lot of value to the web.
tl;dr I suspect Google wants all its services integrated with social because it is trying to build a trust network.