No, this is not right. In my UP game, I was unable to create more than 3 sea trade routes due to the size of my only European trade port. When I noticed this, I set about a plan to capture another province with a trade port, but that was going to take a while. In the meantime, I opened up land trade routes with 2-3 other adjacent factions. By your account, this would have required me to get an extra 3-4 trade route slots via ports before I could open another one. This is not what happened. I eventually got my extra trade slots by spawning a new port town and building it into a commercial port. As soon as the most primitive level of port was ready, I was instantly able to open new sea trade routes, even though my land trade routes had increased while I was previously capped.
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