I agree completely that there is nothing like the real thing, and I love it. But I have three reasons for not using a real Rhodes:
a) the weight of a real Rhodes. For rehearsals and gigs you can carry a suitcase 73 some meters alone, but not more: the weight/size requires two people to carry it. I can put my Fantom X7 plus my Access Virus TI keyboard into a normal car without any problems and put them on their stand within minutes without any help: all not possible with a real Rhodes plus other (vintage) gear.
b) the keyboard action: over the years keyboarders did a lot to enhance it, but even enhanced it still has a very stiff kind of action. I prefer having (most of) the sound, but playing it on a semi-weighted keyboard.
c) output and effect routing. When playing with a band you need a lot of fast switching between different sounds, even within songs. With a real Rhodes this means you have to carry it plus find a way to level its output signal plus add (manually operated!) effect gear, perhaps plus send it into real tube gear like a Twin Reverb. And then you still need other keyboards and have to build the typical keyboard 'castle'.
If you can have all this together with many of the other sounds you need in a device with fine live settings, it is clear why workstations are that popular. And concerning horn section: I simply have none

If I had room and money for a fine vintage studio, you can bet that before anything else a Rhodes Mk I and a Minimoog would be part of it!
P.S. Just saw that Arjan already answered: I agree with every word he said...