Well, for vocabulary read "colour gamut" which an ICC Profile describes. As for using the right profile for the output press... Actually that's not it either, although it's much closer.
A press doesn't have A profile. a rip doesn't have a profile. A profile describes all the colours that can be created on a machine/ink/media/settings combination. I have a dozen profiles for one single product. Although my clients are welcome to those profiles (useful for soft proofing) I don't suggest they work in those colour spaces. The same reason applies as I offered above. Let's say a design is today being printed on a media that takes little ink, has a small gamut. If you work in that space you've limited your artwork to that colour gamut. That only makes sense if you're never going to want that design on anything else, or have it printed anywhere else. Otherwise you're limiting colour for no reason.
This is where colour standards come in. Using something like FOGRA39 makes sense if you're sending to printers that calibrate their presses to match the output standard that describes.
But, and here's the interesting thing for us nerds, any press that can be calibrated to that standard is presumably capable of hitting colours that are outside of the gamut of that specification but is being restricted so as to not do. That's giving away some colour capability isn't it? Anyway - I've digressed from the thread.
I think the conversion responsibility should always lie with the printer and this is why. The printer will be converting to their output gamut anyway! So if the designer does a conversion it's an added, entirely unnecessary stage in the process. A printer who knows what they're about is going to do a conversion on your converted file... I think you're right that good printers should offer advice on colour communication. I don't think asking the designer to do the conversion minimises shifts - I think it minimises surprises and awkward conversations when the blind are leading the blind. Most arguments seem to be about making the printer's life easier, not the designer's. Isn't that just wrong? Who is supposed to be the expert on the printing part?