Most of the big companies opt for the dedicated server. Is there any specific reason for that?

One of the reasons Big companies choose to outsource dedicated servers is the availability of high powered networks from multiple providers. As dedicated server providers utilize massive amounts of bandwidth, they are able to secure lower volume based pricing to include a multi-provider blend of bandwidth.
To achieve the same type of network without a multi-provider blend of bandwidth, a large investment in core routers, long term contracts, and expensive monthly bills would need to be in place. The expenses needed to develop a network without a multi-provider blend of bandwidth does not make sense economically for hosting providers.