Some responses. I guess I have the gear here to create a camera profile, but I've never bothered, for two reasons. First from what I've read, the lighting in which you shoot the colour checker card is critical. It has to be absolutely even, and I guess the colour temperature is fairly critical as well. Second, I don't see the point, for most people. A camera profile may assist you to get prints closer to real world colour, like in your red jacket example, but how many people outside of advertising really need that?
There is a difference between accurate colour and pleasing colour. Take the recent Fuji X-trans cameras as an example. They have been really popular because of the colours they produce. The camera has a number of options to imitate the look of classic Fuji films, like Astia, Provia and Velvia (yuk!). Some people who used to be RAW shooters have found that they can now shoot JPG, because these simulations are so good. Alternatively you can shoot RAW and LR has (approximately) programmed these simulations into the camera calibration tab. But no-one is claiming that these are accurate colour, rather they're pleasing colour, designed to give a certain "look". As the original films did also. (For readers using C1, PhaseOne doesn't include them, but you can download C1 compatible profiles from a thread on DPReview.) The same is true for my Nikons. The cameras have certain look profiles and you can download and install more. Most of these are in the LR camera calibration tab. Again, not real world accurate, but designed to give a certain look. When I edit an image, I'm aiming for an image with pleasing colour, especially skin tones. Rarely would I try to match the real world original. Last night I did a big indoor live theatre shoot, and all I'm trying to do with those shots for the client is make them look realistic, as best as my mind's eye can recall. Real world matching is not practical in this case.
Where you do need accuracy is in soft-proofing, as you've discovered recently. I want to be sure that what I see in a soft-proof on my screen is a fairly accurate representation of what is going to come out of the printer. Which brings us to your Initial post. For my part, although I don't use LR for printing, I still can't see any problem in printing from it. I am assuming that you're printing from RAW. Here is what I understand to be the current word on LR working colour spaces: https://helpx.adobe.com/lightroom/help/color-management.html . LR uses ProPhotoRGB in the develop module, and AdobeRGB elsewhere. You can soft-proof in the develop module, and in the print module you can specify a printer profile to print from. What is it that you could do in Photoshop that you couldn't do here?
In another thread, Jon said "Adobe Photoshop arguably has better color management than LR5 - although Adobe is trying hard to equalize them in more recent versions of LR. In LR5 you are unable to set the working space as Adobe RGB 1998 - but you are able to select the output profile to our ICC for the R3000 and Epson PGPP paper and the rendering to relative". I don't understand these comments. I don't have a problem with the working spaces for printing from RAW. Perhaps he is referring to printing JPG or TIFF, I'm not sure.