I have had to work with applications that designed their api as you propose. I now write REST APIs, because of my experiences with the older-style APIs. What you're proposing is what used to be pretty common practice about 10 years ago. The web has since learned and now knows better.
In the end, the way you propose writing the API is not easier. It's harder. For everyone. Manipulating long query strings and using nothing but GET requests is cumbersome to write, harder to debug, and doesn't actually buy you anything over using a REST model. Having a single entry point in an application of any complexity is not a win -- it's a loss. Ever try to sift logs of an application like that to find something meaningful? It can be done, but I'd rather just find a "DELETE" in my logs than 'method=delete'. In reality, doesn't 'method=delete' seem a little redundant when you know that HTTP already has a DELETE method? Why write code to implement something your web server MUST support in order to even claim it supports HTTP? That's just silly!
Writing a REST API, in my experience, has always meant less code, a more straightforward implementation, and one that is much easier both to test and to debug.
From the standpoint of the person writing code against your API, the same benefits apply. Less code, more straightforward, easier to test. When I work with coders writing against my API who are having issues, determining the source of the issue typically involves comparing the output of a 'curl -XDELETE' call with the output of their code. No, really -- that's it. If curl works and their code doesn't, it generally removes my API as the source of the problem.
There's also no messy parsing of information in the body of the HTTP request. In a lot of cases, the calling code can get the most important information from the headers. If you call a PUT or DELETE method, you mainly just want to know if it succeeded, in which case you read the HTTP status code in the header. This also has the side effect of making things faster, because there is no parsing to do outside of the header in those cases.
If you've only ever written APIs the way you propose, I can kind of understand the hesitance, but you will find that proposal silly the first time you deploy a real, production application using REST.
In short, a single entry point isn't simpler, isn't more efficient, and has zero benefit (and only more problems) when compared to a REST API.