Re maintainability - it is not clearly false. The biggest problem with maintenance is figuring out what the code does in the first place. When you know that the code you're looking at has zero data dependencies other than its arguments, and what's more, cannot possibly introduce other data dependencies through any of its descendants in the call graph, it relieves the burden immensely.
Re adding and removing side-effects: I think you're just making this up without much experience. Most programs only need side-effects in certain areas, typically in the outermost loops and top-level functions. For example, a very simple single-threaded stateful web server could be implemented only needing I/O access in its outermost loop, implementing its request -> response function in a pure way, and using tail recursion to maintain state between different iterations of the server loop.
Re compilers: unless you've written several compilers, you can't make claims about techniques used in compilers not being highly useful in solving large classes of problems. In many ways, yes, compilers are the ultimate functional programs (output is a pure function of input), but guess what: the flow of a compiler - parsing input, inferring its semantic intent, performing required transformations and generating output based on recursive application of patterns - is exactly the same as the flow of an average web request.
Re adding and removing side-effects: I think you're just making this up without much experience. Most programs only need side-effects in certain areas, typically in the outermost loops and top-level functions. For example, a very simple single-threaded stateful web server could be implemented only needing I/O access in its outermost loop, implementing its request -> response function in a pure way, and using tail recursion to maintain state between different iterations of the server loop.
Re compilers: unless you've written several compilers, you can't make claims about techniques used in compilers not being highly useful in solving large classes of problems. In many ways, yes, compilers are the ultimate functional programs (output is a pure function of input), but guess what: the flow of a compiler - parsing input, inferring its semantic intent, performing required transformations and generating output based on recursive application of patterns - is exactly the same as the flow of an average web request.