The precise mechanisms governing the creation of monarchies is really not my area of expertise. The rules (such as they were) differed substantially depending on time period and region, and there are likely individuals here who are far more qualified to comment on such nuance than I am. The short version, though, is that in the High Middle Ages you generally couldn't just declare your territory a kingdom. You needed some kind of societal permission, often given by the Pope, to recognize your newfound authority, especially as king's were technically semi-divine. For a practical example of this, you should look into Roger II of Sicily and his elevation to King of Sicily in 1130.

It is worth mentioning here that 'principality' was pretty much equivalent to 'duchy', in that duchy's were a kind of principality, so Bohemond's title of Prince was roughly equivalent to that of Duke. So, essentially Bohemond was taking as high a rank as he could, since he couldn't realistically declare himself a king. That Antioch was a prestigious city of great historical and strategic significance helped him greatly in his positioning himself as a Prince. Antioch had a Patriarch for example, making it a city of great significance to Christianity, but it also had no history of monarchy (as compared to Jerusalem) and so no practical claim to that highest of titles without the church interfering to elevate Bohemond, something it wasn't going to do seeing as he was actively causing disruptions with they Byzantine Empire.

As to Edessa, Peter Frankopan has recently argued that Baldwin I took control of the county in the guise of a legitimate agent of the Byzantine Empire, taking on the position and rank associated with that regions governor. While that rank would obviously have been in Greek, Count is the equivalent translation into Frankish/Latin terminology. Traditional arguments generally describe Baldwin's actions as more akin to a hostile takeover than a semi-legitimate transition of power (not even Frankopan is prepared to overlook the very convenient death of Baldwin's successor entirely), but even here it is likely that Baldwin would frame his rank as that equivalent to the land he was taking over. He was stepping into an existing position, albeit one he rather conveniently had vacated for him, and with that came a certain level of status. Given his rather limited control of the region, and the social expectations of his peers, it made sense that he would not attempt to claim a rank above his station, especially as Edessa has none of the historical or spiritual significance of Antioch (at least in Crusader eyes, we could debate both cities excellent merits I'm sure).

I suppose the short answer is that they didn't claim those ranks due to a combination of social expectations governing what qualified a ruler for a certain rank, and the pre-existing status of the territories they conquered.

Refs:

Thomas Asbridge The Crusades A great general history of the subject.

Peter Frankopan The First Crusade: A Call From the East, the First Crusade from a Byzantine perspective, it's not really an entry level book, but is a great companion to a more Western-centric history.