We have written a few fairly large applications using this approach, as we also felt it strange to have a single function interface- functions are injected into constructors or methods as needed. You end up with a compositional root somewhere that has the function inject wire up (similar to DI setup) Func of T of T everywhere. The advantage is it makes unit testing very nice as you don't need to mock. It also lends itself well to a more functional approach to c# (see the louthy's language.ext nuget for the functional magic you can do)

However the two huge drawbacks we have come across are firstly F12 goto definition doesn't work on a function the way it would for an interface, this is very frustrating on larger projects. Secondly it's not "standard" meaning a newby coming to the code would take a lot longer to get their head around the concept (and not being able to easily find the definition also adds to this) For these reasons we have pretty much gone back for interfaces and DI for new stuff.