I have never used a website like that. If their system is only web-based, it has not much sense. Only if they have a physical print delivered to you as a reference it can work.
Having a physical catalog of well-defined values and a combination of inks for a specific system is recommended.
I usually use one I made https://otake.com.mx/Color/RGB-01-Letter-LowRes.png for example when I am using a new color printer in the office. I will address the RGB model later. (I can't find my CMY chart, because I don't use it much)
The purpose of these things is to have a physical reference of how a color looks when printed with (I repeat) a specific system.
The most popular standardized system is "Pantone Bridge" https://www.pantone.com/products/graphics/color-bridge-guide-coated. Which gives you CMYK values of a set of originally defined Pantone colors. (With American color profiles)
When I use the CMYK system to pick colors, can I pick colors randomly?
Sometimes people could prepare a defined palette, because they want to focus the design harmony on a set of colors, instead of a chaotic party of millions of random colors. Then they can limit the palette to 3-6 colors for example.
So, I am assuming you refer to "randomly" to the values, not the chosen palette.
Yes and no.
You are not limited to a value of C50%, you can use C49%, C48% or whatever number you want. But you will hardly notice the difference between C49% and C50%, so you can make your life easier by limiting the numbers you use. You can limit yourself to multiples of 10%, or 5% for example. In light colors, you will notice a 5% increment more than in dark colors.
The test image I linked has 20% increments because I am lazy and did not want a super detailed reference. But easily you can choose a color between two samples.
The limitation is the TAC or Total Area Coverage. This number is defined by the print system, normally 300%-330% as the maximum. So you do not use C100M100Y100K100 ever.
There are other self-imposed limitations like do not expect a C1% to be really printed.
RGB when designing for print.
Yes, it is a correct process if you know what are you doing. Some reasons to do it.
- The medium is going to be printed on a digital system.
- You have a lot of RGB colors that need to be included, like a background of a photo that needs to match a text or a graphic element.
- You will have a digital version.
- You are controlling your palette, color conversions, color simulations, and color profiles correctly.
- You need rich blacks defined by the color profile.
- You do not need automatic overprints.
- You keep an eye on your black small texts.
- Your images are provided as RGB, need effects and filters, and you want to keep them on RGB until the export process.
- You still do not have the CMYK color profile defined.
- And some more...
CMYK when designing for print
I must say that you also need to know what you are doing...
- Your output really needs CMYK, like offset lithographic print.
- You have specific values you want on a controlled and standardized system.
- You need automatic overprints.
- And some more...
Some other ways to select colors when designing for print
You can also use spot colors when designing for print, either to be used as spot colors or let the conversion for later. You usually use a Pantone Formula guide or similar for spot inks, or Pantone Bridge if you use the system often.
You can even design in black and white and put strawberry ink when printing. In this case, you normally have close contact with the print company directly, and you can be on site to see the strawberry color.
Sometimes it's "safer" to design in RGB for print, and sometimes is easier. CMYK and spot colors are more specialized. You choose whatever method you need when you need it.
P.D. You can notice in my comment that I can not find my "CMY" chart and not the "CMYK" chart. And you can notice that the link you provided almost does not use the K channel.
Using or not the black channel is trickier than you might think.
P.D.2. I do not use much the CMY reference because I only use it in a few cases. As I said, when printed on offset lithography, that means that I got 1000 prints. I used those as a promotional items. Besides that, you do not do that many times. I do not change the print company often. I managed to stow away it on a project that had some free space on the sheet. On digital prints, the colors are less vibrant. As I have done that many times with similar results, I only send one RGB print. I don't need to compare it vs the CMY chart anymore.