I don't have hard data but would love some as this is the center of a proposal I'm now writing.
In my case, I turn the conversation back to business goals. The purpose of social media for this company is to drive people to their website. If people are on the home page and we send them away, then we're working against those goals. The staff prefer social media because their CMS is in the way, it's just easier from workflow to quality standards POV to post to Facebook. I have to point out what they're are losing by not investing in the website first - real, engaging shareable stories that people and the press want to share. None of the social channels facilitate any meaningful transactions for them. They want to see dollars, not more likes. I'm presenting this as challenge, tracked by analytics. They already know they can produce content for social channels, can they produce content for the website that brings in more visits, more multiple page visits and lower bounce rates?
Usually I find this conversation is political and sometimes, you have to
give in or find a compromise. I think making very clear you have social media is great. Don't hide it, make a prominent graphic appeal. Or add it as "continue the conversation on ...." to the actual body of a post. Call to Action leads to social media, great.
Is there data that is unique to your context? What do numbers of followers and likes really mean to your leadership? Is this tied to someone's evaluation or departmental funding? Is it an experiment a higher up wants to see done? Are your major competitors doing it - because if their not it's a sign, you can look at all of their numbers and what they're doing. Social channels take lots of time to develop audiences and community. If you're not seeing numbers there, taking it to the home page will only detract from the home page's function (meaning turning people away from sales.) Better to use the channels to find customers and start conversations and relationships. Use them to generate new leads - don't send away the ones you already have.
In my case, I work for non-profits who know social doesn't generate ROI.
They use them solely for good will and community building, my challenge
is to convince them that web content not social media that generates
press, participation and donations. This can be harder to business
leaders to understand but there are lots of articles - Forbes, Forrester - on how social doesn't create leads or sales. Kissmetrics, Boagworld sometimes.
Today's Forbes article is another in the series of how social doesn't bring in direct business
http://www.forbes.com/sites/meghancasserly/2013/04/17/why-small-businesses-are-losing-on-social-media/ Sometimes you just need one powerful stat.
Or a back-up plan - like if social goes on the home page you will agree to rigorous analytics review and remove if negative impacts are seen. Figure out how the current home page's analytics are working first :)
Hope this helps, I'm very interested to hear from folks.