Depends on the game you want to run and how much performance its engine needs. Some games would probably run fine on a Pi; some games would need a more powerful system. Some arcade systems supported by MAME have more processing power and specialized hardware than the Pi itself, even before taking into account the overhead of emulation.

But beyond that, a commercial MAME cabinet would require ROMs. People have built unofficial cabinets of questionable legality incorporating a pile of ROMs, but a commercial cabinet would require actually licensing specific games.

It's also worth noting that the main goal with the MAME project is preservation, which means that the focus is on the accuracy of emulation rather than the speed of emulation. There are other arcade emulators that offer faster emulation speeds for the games they support, such as Final Burn Alpha for Capcom and NeoGeo arcade games.

In particular, some of the 3dfx emulating machines etc are absolutely brutal on the CPU for emulation

Sorry, I downvoted you by accident, can someone else please upvote to correct this.

Done.

The Pi doesn't have the power to run some games.

I ran into problems with NeoGeo games.

Were they borderline performance issues, or were speeds off by an order of magnitude? Would they run acceptably on a Pi3 (about 1.5x a Pi2 and 10x a Pi1)? What about an ODroid-C2 (about 1.5x the speed of the Pi3)?

Nintendo64 and Playstation emulation on ARM SBCs is probably in a similar state, for a lot of games. Some games will run beautifully, some will be hopelessly slow.

Completely unplayable on a Pi2. When it didn't do the hardware bootup after 5 minutes, I gave up.

Maybe the ODroid could make it happen but the Pi2 simply cannot.