Well, there is a trading port on the eastern side of the Neck, it’s White Harbor. Which has a first mover advantage that would probably put the kibosh on any competitors.
And yes, Saltpans and Maidenpool should be more important. The story here – as with Duskendale – is the lack of royal charters inhibiting development. In the case of Saltpans and Maidenpool, we learn that there was “a tendency for the kings of the past to refuse the charters that might have given some Saltpans or Lord Harroway’s Town or Fairmarket leave to expand.” (WOAIF, p.151) This is possibly because the Kings of the Rivers and Hills weren’t that secure in their powerbase and wanted to ensure that the more easterly parts of their realm (in the case of Saltpans and LHT and Maidenpool) or the former capital of a previous House (in the case of Fairmarket) didn’t get too powerful and challenge the Kings for supremacy.
The question is why didn’t this change when the Targaryens came? Well, as with Duskendale, the Targaryens weren’t interested in letting other cities “vie for trade with King’s Landing,” (WOIAF, p. 118) as the Iron Throne gets 100% of the income from King’s Landing trade and would get a smaller cut from any other lord’s port. Given that every city in Westeros predates the Targaryens, I don’t know that there’s any examples of a Targaryen monarch giving a city charter (not a town charter, the two are different) and creating a new city.
In fact, if you look at Targaryen development policy – most noticeably the royal highways built by Jaehaerys I – the whole point is to route traffic through the capitol. Thus, the River Road abruptly turns south at Lord Harroway’s Town straight to King’s Landing, rather than continuing along the bank of the Trident to Maidenpool; Maidenpool in turn is on the Rosby road, so that you have to travel to King’s Landing before taking your goods anywhere important via roads.
So I think the story here is the weakness of the post-Draconic monarchy driving policy to favor the King’s personal income and thus the capitol. If the Targaryen monarchy was more of a genuine nation-state, you might well see the Kings doing more to promote economic development more widely.