Mame can convert analog joystick input into the digital input that is expected by a particular game, so in a sense it is the perfect mame joystick. Furthermore, if mame's conversion doesn't quite fit your needs, the Ultimarc stick has a config utility that will allow you to design a map for conversion from analog to digital.
Two reasons analog joysticks are not universally considered the perfect stick are that you don't get the mechanical restriction of movement that you would from a 4 way joystick (i.e. preventing you from moving it diagonally), and that you can't "feel" where the stick engages when you push it (though you can't with leaf switch joysticks either).
But if having just one stick is more important than the arcade authentic feel, then that is certainly the way to go.
On the other hand, there are sticks from GroovyGameGear and Ultimarc that are switchable between 4 way and 8 way from the top side of your control panel so in theory these could be the "perfect" stick. However, in the case of the Ultimarc stick (Mag Stik Plus), the 8 way mode is almost useless. I love it for 4 way mode and would recommend it for that, but the throw is so short that in 8 way mode it's hard to keep the stick out of the diagonals. Not sure if the GGG stick has the same problem.