tl;dr - What are the advantages of having handler and service methods separate housed in separate classes, rather than joined in a single class.
Background
Salesforce and others reference using Service classes as part of a best practice breakdown of class and trigger architecture. (Trailhead example, stackexchange example, third party article example)
The premise seems to be that Triggers handle "when" the automation launches, a handler class handles "what" launches, and the service class handles "how" the automation works. I understand the basic ideas behind dividing functionality into distinct areas, but the separation of a handler and service class seems a bit excessive to me.
A practice I have been doing for a little while is simply having the "stoplight" considerations at the top of a handler class (aka, what fires when), and then below the stoplight code is a comment in the code stating the service methods are below, followed by the various service methods. The advantage I see in this model is that I don't have to have multiple files open, and can easily do text searches across my single file to locate code.
Question
Since there is so much written about the service layer model, I imagine there is something I'm missing here, and was wondering if anyone could explain the clear advantages of having handler and service methods separate, rather than joined in a single class.