The chief pro of salt bath is the precision and consistency with which the heat can be applied. Modern digital controllers that cost 25 bucks can hold temperatures to within a degree. Heat transfer rates from a liquid to a solid are orders of magnitude higher than gases to solids, so if you immerse a case to a certain level annealing will take place in the immersed regions almost instantly, while areas just a couple of millimeters above the liquid line will take several seconds to anneal. You know what a .22 TCM is? Try to anneal of those, or even a .22 Hornet, with a flame and consistently anneal just the neck. With salt bath it's a piece of cake.
The biggest con currently will be availability, particularly of the salt. I sold the kits and supplies from 2017-2022; I was buying the blended salt from Park Thermal in Milton, ON. But then Park dropped the salt business and suddenly I had to buy from Durferrit in Germany. The salt from them was ground much finer and raised a lot of dust. The paper packing absorbed moisture and allowed the salt to clump. And the price doubled. You can try to make your own but potassium nitrate is regulated as an explosive precursor and sodium nitrite is regulated as an aquatic toxin so it will not be easy. The other bits and pieces I manufactured can be replicated but honestly the tools and designs I had were, in my opinion, pretty slick. Something you cobble together probably won't work as well.
The cons side of the equation got worse when I used my resources to really dig into annealing. I confirmed to myself that virtually everything shooters think they know about annealing is wrong. It was difficult to market a product starting with the premise that the customer has to be re-educated. And I had no interest in simply repeating the falsehoods to drive sales. I never once mentioned in my promotions or on my website that salt bath annealing could improve accuracy. But I was acutely aware that most of my customers were buying it for that purpose. The induction systems caught the imagination of a lot of people, sales of salt bath stuff went into decline so when the salt became a headache I just abandoned it. I see kits pop up on the used market from time to time, but the salt does run out eventually. You get something like 5000 cases annealed per jar of salt.
I completely agree the need is overstated. The only proven benefit of annealing is to prevent neck cracking. Neck cracking is caused by corrosion in storage. Whether or not your ammo suffers depends on where it is stored, and how long, which is why some people experience neck cracks and some do not. I used to get about 80% neck cracking every spring of the .223 and .308 ammo I had reloaded the previous fall for my AR15 and M14 rifles. If you are not experiencing something like that, you probably don't need to anneal.
I hate this approach. Given the high conductivity of brass, the cases go from perfectly comfortable to painfully hot faster than human reaction time, meaning you will cause yourself physical pain with each and every case. Why would anyone do that? Count the seconds or watch for colour change or something.
Salt bath uses nitrate salts, which are essentially non-corrosive to iron and copper based metals. Priming salts, road salts, sea salts and table salts are chloride salts and yes, they can cause significant corrosion.
For those who do want to anneal, I would also recommend an automated flame setup of some kind for most cases. The truth is the fantastic precision and consistency of salt bath is not needed for most applications. The window of temperature that relieves stresses enough to prevent stress-corrosion cracking without affecting the case microstructure is huge, 450-600°C. And frankly, I've seen no evidence that "overheating" the cases to 800°C causes any real problems (induction annealers do it all the time).
Admittedly if you've got a .22 TCM you're kind of stuck.