For anyone working with print there is one key principal to keep in mind: "CMYK numbers" are meaningless. Far too often artists are lured into "working in CMYK" without actually understanding what it means, and fall into the trap of believing their work is more precise when the exact opposite is true. Saying "50% Cyan" does not actually specify any color, and will most likely result in many different colors being produced. The subtle yet critical difference between "untagged CMYK" vs. "unspecified CMYK" is the bottom line that will mean the difference between success and failure.
CMYK is a type of colorspace, but in and of itself does not actually specify anything. It just tells how one can define a specific colorspace. To actually make sense a specific device (either real or theoretical) needs to be targeted. Once the specifics are involved, however, working in a specific CMYK is a very helpful thing. It is good to try to not get caught up in distraction of focusing on the "how" of things and instead look to the "why" of doing things.
In this case, the distracting "how" is people "working in CMYK" while the "why" they should be focusing on is reliably creating and controlling color. Instead of an artist getting caught up in saying "I need to get exactly a 50% saturation of cyan ink onto the printing plate at this point", they need to shift to say "I need to get this point of the final print output to be exactly this shade of color." That is not to say that an artist should never be concerned about CMYK numbers and plate separations, but rather they need to keep in mind that the ink details are merely a means in reaching the ends of the final print. (There is one main exception to the focus on raw CMYK, but I'll cover that later)
So although 'raw CMYK' numbers might be meaningless and produce randomly shifting results in completely unpredictable ways, CMYK values in a specific context normally give very precise and controlled output. Be wary of anyone asking for or providing "generic CMYK". However, specifics such as "SWOP v2 CMYK" will allow for fairly exact control and results. If someone says "CMYK", the response should be "which CMYK?"
What does this all mean in practice? If one is producing artwork that will go to print, getting specifics nailed down is critical. When working with a good print house, they will provide either specific profiles for the output that will be run, or will say which industry standard profiles they will work from. The artist provides content targeting the specific CMYK profile and then the printed results comes back with the exact appearance that was intended. The print house gets this generally specified input and then does a specific conversion from what the artist supplied to the measured control needed for the specific press and the actual paper with that days inks and the current temperature, humidity, etc.
When such a good workflow is used one can get reprints run at any time later on and the output will match what was printed the past week, month or even year. Thus there is no need for the time nor the expense of multiple tweak-and-reprint runs to end up with acceptable results.
On the other hand, if a small shop is used that employs no color management in their own workflow, the burden falls squarely on the artist/customer to come up with ways to get consistent and desired output. Sometimes the print shop will provide some target profile, but make no guarantees as what the resulting run will look like.
This is the point where most will just think they're working directly with raw CMYK and just need to tweak things over and over until they are close enough. That's actually not what they should be doing. The critical need here is to understand that they are not working in "generic CMYK", but that they are working to a very specific CMYK. They really are working in "CMYK for fliers printed at the corner press". Sometimes that color will be consistent over time, but more often even that will vary from week to week or from day to day. If the artist was smart, he would have created his own profile for the local print shop and will work in an industry standard CMYK and convert to the specific local shop CMYK for delivery to them. He also should have done some simple calibrated output (perhaps in the margins of his run) so that if (or more likely when) the local print shop gives different colors for the same numbers he can call them on it and get things corrected.
For a shop with a good relationship, the artist can use his own management and tracking to get the print shop to correct their output. Some small shops might not even be employing much in the realm of color control but can happily match output to a reference proof they get handed along with the files for the job to be run that day.
Finally in the case were the local print shop will give varying results and no help for color matching we reach the situation I mentioned where actually sending raw CMYK values is desired. However the reason for sending out a file with raw CMYK that is intended to go exactly to the end plates is in creating a test target output for measurement so that the artist can create his own target CMYK profile. The artist can send over a raw file to get a test output print, and then measure that test print. He then converts the real job files to using that locally created profile and sends the adjusted art files over to be printed. The net result is better output with lower costs due to avoiding reprints, etc. (so "raw CMYK values" should really only be used for printing test targets)
This last case helps illustrate the difference between "untagged CMYK" and "unspecified CMYK". The artists sends over art files that are not tagged with any embedded ICC profiles. However these are not raw nor "unspecified" CMYK values at all. Rather they are CMYK numbers in the specific profile that the artist himself has created to describe the characteristics of the local print shop. Although the files are not literally tagged with the profile, they have been created with an explicit ICC CMYK profile specified in the artists workflow.
And the bottom line? Be specific and you will save both time and money. And end up with happier clients.