However, be careful not to lose sight of the business value those client side integrations of Facebook / Twitter / YouTube may be providing. Many "widgets" that allow you to like, tweet our view content also come with a buffet of analytics especially written for browsers. You may lose out on tasty marketing features provided by the integration partner by sterilizing their API behind a gateway.
Optimally, I'd say do both in moderation. Don't blindly rip out your Facebook like buttons without first looking into some good
tag management solutions. Proxy or get rid of the poorly performing tags and give priority to the ones that give you a competitive advantage.
Most API Management vendors will have different approaches to accomplish this (FB / Twitter Mashups), and all of the ones I've reviewed are perfectly capable to perform what you describe (and come with examples).
I'll leave you with this final note. When I've considered mashups on my internal SOA, the burden of latency ends up really hurting your SLA. The physics of moving those packets back and forth to on your internal bus will hurt your response time one way or another. Cloud based Web API Gateways offer a big advantage here have have been purpose built for the task.
My 2 cents.