I don't see anything wrong with a USB HID interface for NES controllers. That's pretty much what AVR-style micros are just right for. Assuming you're using an AVR board with a native USB uC of course, like a Teensy++ or similar. I've done similar things myself, both using custom PIC designs and off the shelf AVR breakout boards. Also, LUFA, which I assume you're using, is great and in general much higher quality code than a lot of Arduino stuff.
If you're using software/bit-banged USB, you really should look into doing it right with a micro that has built-in USB. But that's by no means the worst micro abuse I've seen (and there is actually an argument for doing bit-banged low-speed USB in super low cost scenarios).
Similarly, although I'm not a huge fan of the Raspberry Pi for other unrelated reasons, it's a perfectly fine fit for NES emulation.
Further, another micro for power management isn't too far off either. It's separate enough that I wouldn't want to throw it onto the micro doing HID. I would encourage you to eventually design a more integrated power control board without using a full-blown arduino for it though, and learn to do it using MOSFETs and the like instead of relays, but that's a learning path. I've used my share of relays for quick and dirty power control.
The abuses that I had in mind are nothing like that. It's things like people using an Arduino to run game logic for a video engine implemented in an FPGA (where they could just implement the micro itself in the FPGA and get something much faster than the Arduino without the Arduino), or, on the other end of the spectrum, people using more than one Arduino to do what is effectively blink LEDs (as a one-off/temporary project it's fine, but if you're doing more than one or doing it permanently you really should stop being scared of using bare microcontrollers and learn how to make your own design closer to the requirements - an Arduino is nothing more than a voltage regulator, a USB to serial bridge chip, and a bunch of wires). Or people building entire commercial products around Arduinos with no particular excuse for using them (like compatibility with other projects/modularity), just because they don't know any better and they are too scared to stick a bare chip on a breadboard.
Yes. I'd probably consider 10 or maybe even 20 to be the cut-off for putting more effort into it.
This tells me that you have the right idea, you just need to get over the mental barrier. I deliberately made the threshold low because it really is stupidly easy to use bare chips. An Arduino is nothing more than an AVR with pins broken out, a voltage regulator, and a USB-to-TTL-serial converter onboard. You can get exactly the same effect by sticking an AVR into a breadboard with a 7805, and an external USB to TTL dongle/breakout board. And since for a great many projects you don't need USB, you can keep that external as a debugging aid only. Voila, welcome to the most basic microcontroller circuit: power and ground. You literally don't need anything else (an external clock crystal is helpful for clock accuracy but not required for many applications).
Personally, my threshold is 1. I will use dev boards for microcontroller design prototyping but if I'm ever making more than one, even for myself, I'll roll my own thing. Sometimes I don't even bother prototyping it with a dev board and go straight to a quick and dirty but stripboard build or similar, if it's a one-off but so simple that I know it will work. I mean, why use a clunky Arduino or other dev board when all I really need is an 8-pin chip for a tiny task?