Brining (old style) was for preservation primarily. Starts at a 10% solution. The kind of stuff where you want to soak in cold clean water for a long while, maybe change it once or twice, before cooking. Think saltier than a store bought ham.
Brining (post discovery of cheap refrigeration-style) is for two things - one, its a method of insurance against meat drying out in dry cooking methods like smoking which involve many hours at temperatures which may (but shouldn't) exceed the boiling point. Second, its a way of imparting flavor - not just by salt. The same chemical/mechanical processes that cause the (essentially) unsalted water inside the bird's cells to equalize with the (comparatively) salty liquid outside the bird and thus bringing salt into the cells will convey other flavors besides. Frequently, herbage or spices are added to the liquid brine - garlic, rosemary, peppercorns, cumin or coriander, bay, dill, etc.
Ever cut open the breast on a Thanksgiving turkey and compared the flavor of the meat just under the skin on the breast (YUM! but sometimes a bit dry) with the meat of the second layer of muscle, up against the keel (BLAND, but moist!). Brining helps address both those issues.
But if you have salt sensitivities, you need to adjust your brine accordingly. Since you aren't using it as a preservative, you can drop it considerably. I make my own corned beef, in a 3.5% brine solution. I've taken it as low as 2.5% - 1/4 of what used to be considered the bare minimum - because my brining occurs under refrigeration. I'm not making pickled beef (or fowl). Look to the inclusions as well - Pink Salt (Prague Powder #1 or Prague Powder #2) is not that overpriced Himalayan stuff full of impurities, it has an antibacterial agent in it in very small quantities (6.25% Sodium Nitrate), the rest is sodium chloride - table salt. It takes very little PP#1 plus considerably more salt (sometimes and sugar) to brine a piece of meat.
Finally, contra claims by many, brining does not tenderize a bird (or anything else) to any notable degree. it merely helps keep it moist. The tenderization of a corned beef (to give a readily understandable comparison) comes from a slow cook process which allows the collagen and other connectives to gelatinize and break down. But that happens at temperatures where the proteins are long past done. How done? A steak is medium rare at about 125 degrees. The brisket coming off the smoker, or out of the crock pot, is done at 175 degrees. Collagen doesn't even start to break down till 160 degrees, at which point your steak is so far past well done the chef should be taken out back and put out of their misery...
Hope that helps!
/edited for coherence.