The key is in fluid compartments and osmotic activity. For the purposes of this discussion, let us say that there are two fluid compartments the ExtraCellular Fluid (ECF) and IntraCellular Fluid (ICF). Only the ECF contributes to blood volume and blood pressure.
Na is not only the major ECF ion, but it is also confined there. The ICF concentration of Na is much lower than in the ECF, and it is continuously, invariably and actively kept out of the ICF. In other words, the vast majority of ingested Na ends up in the ECF, and drag the associated amount of water (ie volume, thereby increasing blood pressure). It is the opposite for K, which is mainly in the ICF. As for Cl, it is more or less equal in the ICF and ECF, and is allowed to move freely between them, meaning that you need to ingest twice as much as a given amount of Na for a similar effect on volume distribution. Bicarb is a minor ion, and moves freely between compartments. These are the reasons why, clinically, if someone is hypovolemic (ie dehydrated, losing blood) they are given a sodium based fluid or a protein based fluid (colloid), because both will drag volume and stay in the ECF.
As for the other part of your question, isn't it tightly regulated? Yes, but extra sodium takes some time to get excreted (much less than 1% of sodium that goes through the kidneys is excreted). In other words, any extra sodium (i.e. extra volume as we have established) will stay there for some time, and if you are continually having high sodium meals, every day, you will walk around with extra sodium most of the time. Therefore, your blood pressure will be higher than it would be, if your diet was lower in sodium.
So, no, sodium is not stealing the spotlight from anyone when it comes to ECF. But the other ions have their glory under other spotlights.