Does the brined chicken get more salty a day after it has been brined?
With brined poultry - especially relatively small, i.e., chicken vs turkey - I think the issue is more the texture. It takes on a sort of spongey deli-turkey feel after too long. (Then again, I find this unpleasant in even a brined turkey, and many seem to like it.)
I have repeatedly commented about my dislike about wet brining poultry here and have received some agreements, but many other comments that my assessment is wrong.
Ultimately, you are the judge. I despise wet brining poultry for the reasons you mention and have discovered that I hate deli turkey for the same reasons. This is not a recent development. I have loathed deli turkey since I was a kid.
Do as you wish.
I'm sure some F52 commenters will say how much they love wet brining poultry. That's fine, more power to them for enjoying it. I do not.
It's your call.
I dry brine chickens (small ones) for 3 full days a la Judy Rogers from Zuni Cafe. Then I let it sit uncovered for one more day to dry the skin. It's by far the best roast chicken I've ever had. I no longer wet brine for the reasons already posted.
I assume you can dry brine chicken breasts for three days as well or would that be too much?
I can't answer that. CV may know. I have only dry brined whole chickens and used 3/4 tsp per lb. In a way, if the breasts are skin on and bone in, you could be right. I just haven't done that myself. If I were to just give it a go, I'd probably start with 1-2 days.
Here is a short blog about the specific method I am speaking about.
I have little experience dry brining chicken parts more than a couple of days. Like Susan W., most of my experience is with small whole chickens.
My gut feeling (unsubstantiated) is that you can go out to 3 days for dry brining chicken parts and that people on this planet have done so for decades (if not centuries). However, this is no endorsement for such procedure.
Note that nothing stops you from dry brining two days, rinsing them off, then letting them air dry in the fridge for another day (like Susan W alludes too).
In my workflow, I don't seem to ever get into this conundrum though.
If you are routinely in the habit of not cooking things when you plan to, I suggest you err on the side of cooking things sooner rather than later.
I think I'll dry brine some thighs that have been in my freezer for 2-3 and let them sit to dry.
By the way, I don't rinse the chicken before air drying. Russ Parsons has you let the Judy Bird turkey sit one day to dry, so I do the same with the chicken. Perfectly seasoned meat with shatteringly crispy skin...and an apartment full of smoke is what I end up with. Well worth it. I may try cooking it in my cast iron skillet outside on my gas grill next time.