Last we heard, they have more immigrants now than original "natives", and the influx of people from trading nations like Arad Doman has totally changed their outlook on trade.

The TR area is already "opening up". It would certainly welcome a trade road to the South, if it was not that aside from Ghealdan, a nearly wrecked nation at the moment (Masema has all but emptied the major cities, a few of which are half burned), it only leads to Seanchan territories...

No major development like the building of a giant bridge over the Manetherendrelle and the deforestation of a large area to build a road are going to happen in the short term anyway (and in the long term, it may well become a moot point, with Ghealdan already absorbed by the Seanchan or perhaps more likely with a diplomatic settlement that will re open the normal trade routes and solve the whole problem of the Seanchan conquests. As far as we know, Jordan meant for Tuon and Mat to go to Seanchan to reconquer it five to ten years after TG, so plot twists are definitely coming on that front). It would be a feat of engineering to make such a bridge at this point (channellers could perhaps make the bridge, but no one probably has the knowledge in engineering to design it... and the knowledge to make alloys and other reinforced materials is still unrediscovered) and it's rather low priority considering that major cities like Maradon have already been razed, Cairhien and the capital of Arad Doman are in shambles etc. - with winter coming after TG and tons of people living in those areas that will need a lot of help from masons, builders, engineers and channellers (and Caemlyn itself was now in major danger, last we heard...not to mention the damages in Tar Valon).

That, and beside, the Seanchan are still at war. It's bad enough they can Travel now, no one is going to make it even easier by providing them with new mundane means to cross North. We also know from Aviendha's visions that if the war isn't stopped soon, it's not going to go well at all post TG for Elayne's alliance or the WT/channellers. They rather loose against the Seanchan, the last remainder from that side being pushed back into the Waste eventually.

So yeah, theorically a trade route north might help Ghealdan remain in the sphere of influence of Perrin and Elayne rather than fall in the Seanchan sphere (and why would that be so bad for Ghealdan anyway? It's the folk's best chance at bringing order and safety back fast, if it were not for TG starting...), but there's just too many factors in play right now anyway to predict how things will stand politically post TG...