What are the general categories of benefits of being part of a denomination? It seems most Protestant churches fall under one of two umbrellas: denominational or independent. What is the general rationale for a Protestant church to be part of a denomination rather than being independent? What general types of benefits are there in not being independent?
Pragmatic concerns

A denomination allows churches to cooperate and share the cost of many things which are needed to support the Gospel ministry of those churches, including: insurance, banking, and other financial services; HR and other personnel services; legal services; child safety; etc.

Doctrinal centering

With all the various theological debates among Christians, it helps to be able to identify yourself with like-minded Christians, and to be able to easily communicate the broad shape of what your church teaches to visitors and potential new members. No denomination specifies exactly everything their members believe, but there is usually enough that hearing that a church belongs to a denomination will give you a reliable idea of the core of their beliefs. For people who are needing to find a new church, it helps to be able to quickly get a good idea of what each church will be like, rather than spending months slowly uncovering each church's distinctives. Denominations don't reveal everything, but they help you form a shortlist to consider more. 

But these denominational identities are not just taken from surveys of what their members believe. In a way they're aspirational. The churches of a denomination know that not all their members agree with everything, but together they believe they can put forward the best case for how they read the scriptures, and will in time strengthen the faith of their members as they grow in their understanding of the core of their doctrine. So I've labeled this section "Doctrinal centering" as I think this is more active than a mere doctrine classification and identification would be. For example, not everyone in a Baptist church will necessarily believe in Believer's Baptism, and that's okay. But the churches that join together as a Baptist denomination don't do so merely because the majority of their members are personally Baptists, but because they believe that their doctrines work to encourage aspects of faith outside of the immediate corollaries of baptism, and that drawing attention to Baptism as they do gives strength to the growth of the Gospel.

In the friendly debates within Christianity, denominations help give structure to our disagreements. As most denominations originated over major theological disagreements, when we want to revisit those debates the denominations remain relevant groupings. They help us work together to put forward the best possible arguments in the debates between camps (such as between Reformed and Arminian for example), as well as giving space for gifted theologians to debate the subtleties of each camp internally, as they consider questions which can be highly important to those within the denomination but may not even make sense to those outside. 

I've seen this in regards to theological colleges. Some independent colleges value giving a balanced overview of what all Christians believe but end up not personally challenging their students as much as denominational or confessional colleges. From the perspective of formal academics this is a great strategy, but from the perspective of faith our colleges should be places which encourage the iron sharpening iron of deepening personal faith. I went to a college where I wasn't part of their denomination, but I believe my faith greatly benefited from being challenged by the more subtle arguments that wouldn't have been presented at an independent college even when I wasn't persuaded by all of them. 

Mission strategy

Denominations help us plan, coordinate, and carry out our God given mission. At both the local and global level, they help us plan how to take the Gospel into every community, so that none are neglected, and so that we don't step on each other's toes unnecessarily. This is not to say that great Gospel work doesn't get carried out by non-denominational parachurch groups, and many of the largest mission agencies aren't denominational affiliated. But they help churches cooperate to run theological colleges and seminaries, to strategically plant new churches, and to share resources so that ministry work can happen in difficult unpleasant places, and not just beach towns and ski villages. Mission strategising can take place outside of denominational structures, but it's often easiest to work together when you know you're on the same page theologically.