That link you posted is quite supportive, with some good sources.
Regarding this or that "displacing" the other, I'm not sold that in all cases its mere numbers of particles that drives "displacement". For example, we take in quite a bit of chloride relative to bromide, yet that relatively large amount of chloride still isn't enough to "flush out" the bromide.
Were it merely a matter of simple displacement, one would expect to be able to flush bromide out using only table salt , which is sodium chloride. The fact that it don't work that way, but requires iodine, suggests chloride can't do it and that somehow Iodine is favored in an equilibrium process that bromide also takes part in on some substrates, and in those interactions iodine, or more correctly iodide, dominates.
With the alkalis on the other hand, we do see where sodium is capable of depleting potassium, the body readily losing its potassium in the presence of added sodium and a diet lacking in potassium, which is bad for reasons suggested in the link you provided, among others. A strong case could probably be made for potassium deficiency providing a fertile opportunity for cancers to develop. Alkalis are a whole other can of worms as they say, one could probably devote a page on cz to their discussion. My main point was to consider being selective in the "salt" one uses, as most folks already take in too much sodium and putting more in, just to get chloride in there, probably doesn't help expecially when other sources of chloride are available, such as the K salt.