I used to think console games on a MAME cabinet was a stupid concept. I definitely don't do it very often, but over time, I've changed my tune somewhat on this topic.
It's definitely true that a LOT of retro console games suck with arcade controls. Atari 2600 games suck in emulation, no matter what. Most Colecovision and Intellivision titles don't work very well, due to the absence of the number pads. Atari 5200 is out, because that joystick was floppy and analog. Tons of NES games were platform-style, which sucks with arcade joysticks. Titles on the SNES that used the shoulder buttons kind of suck.
But, there are some types of games--namely, shoot-em-ups and beat-em-ups--that not only work great with arcade controls, but, IMO, feel better than when playing them with original controllers. I realize many of the games that fall into this category have "original" arcade versions that could just be played in MAME--which is usually what I would do--but every once in a while, playing old home console ports can be fun.
It's kind of like listening to a cover version of a song you like. For example, I love Robotron and Food Fight on the Atari 7800; in fact, when playing on the cabinet, the 7800 version of the latter is much better than the original due to the fact that the 7800 version is meant to be played with an 8-way stick. The 7800 version of Robotron supports the dual stick control scheme, which is kind of tough to do on a real console, and the game itself is really quite good.
As another example, I love playing Robotron X (from the original Playstation) on my cabinet. I'm able to set up classic twin-stick controls, whereas, if I were playing on original console hardware, I'd need to use the buttons to shoot (boo).
I've got a few retro consoles, but unfortunately, I find that most hand-held controllers from the 16-bit era and earlier cramp my hands, especially when button mashing is required. Arcade controls help immensely in those cases. I know most old consoles have "arcade stick" peripherals, but come on, those aren't the same. They're cheaply made, they slide around on your lap, etc.