Welcome to the rabbit hole. I am not saying that every single program needs a profile, but what I am saying is that one profile does not serve all purposes. This is a complex subject and I do not claim to be an expert, but let me provide a bit more context. For the sake of discussion, let's divide this subject into two topics - color space and calibration. Hardware and software work in color spaces. The least common denominator of color spaces today is sRGB. It is a somewhat narrow space, but it is generally what is assumed to be the space on the everyday Jane and Joe's computer. There are wider color spaces, like Adobe RGB and ProPhoto RGB among others. Good editing software likes to use a wider color space if possible as it provide several benefits in the editing process. One significant one is that it maintains as much color from the raw file (which has no assigned color space). Generally, you want to start with the largest workable color space and stay there as long as possible before needing to move to a space like sRGB. Some programs allow you to change the color space they can work in, but in general, it is best to work in the recommended space, which is usually the largest workable space. LR, for example, uses a variation of ProPhoto RGB called Melissa (named after one of the original program authors). Now at this point, you also need to know that raw photos, which have no assigned color space usually contain an embedded jpeg file that the camera creates for convenience. This the file that you frequently see outside of an editing program when you are browsing. This is important because that jpeg file is created based on what the camera manufacturers want you to see. It is neither correct or incorrect. It is just what they selected. The reason this is important is that folks see this embedded jpeg and then they see the raw image in an editing program and they often do not look alike.
With respect to hardware, monitors have color spaces they are capable of displaying. At a minimum, if you are editing images, you want a monitor that can display 100% of sRGB. Wide gamut monitors can fully display 100% of Adobe RGB and some can display a few other spaces that are becoming more common. I am assuming that you are not using a wide gamut monitor, so I am not going to go into the detail of how that can impact your viewing of images, but know that this is there and needs to be accounted for if you own one.
Now on to calibration. Calibration is basically getting hardware to display colors in a known state. Monitors and printers need to be calibrated so that the color in your file is seen as it should be in the color space you are using and and printed the same. Printers and monitors usually need to be calibrated and then have their own correction files created so they can be corrected at start-up. The corrections for once device do not serve as corrections for another device, and that is why I said that one file does not serve all purposes.
Finally, as you move through color spaces in your workflow, hopefully from larger to smaller, you need to be aware of colors that will be flagged as Out of Gamut. This means that a color that appears fine in Adobe RGB is not going to be able to appear as such in sRGB. There are ways of making that color appear, but that involves a bit of "crunching" to make that happen. But, this is also a reason why images can look good while editing, but not when viewed in a browser, especially if the viewing program is not color managed.
My apologies if in my short handing this explanation if I made any errors. As I said, color management is a vast and complicated subject, and one can easily get twisted around, evenif they do have an idea of what they are trying to do.
Good luck,
--Ken
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