There isn't enough Marsh for it to dominate a region -- at least not on any of the Firaxis maps.
Approx 8% of grass tiles turn to marsh. For there to be more than about ten plots of Marsh on a Standard sized map is rare. They are usually clustered in to patches of several, though. (And any Sugar in Jungle turn the tile in to Marsh).
If a request to place a civ near Marsh had crossed my desk, it would have been doable. But "doable" still has to interact with a particular map instance and fit in with all the other bias needs. I would have had to create a new Regional category called Marsh, and then I would have had to give any Marsh regions a second rating as whatever they would otherwise have been -- so we don't lose functionality in the process. It would have been a little bit tricky and sucked up time away from doing other things.
A mod to add this could be done if somebody cared enough to do all that work. But the likely outcome would be very little change. Start points wouldn't get moved at all, so the odds of one happening to plop down near the marsh are very low. Marsh is bad terrain, so start points would generally try to avoid being near a bunch of it.
A better answer might be to fudge the tiles. When Netherlands is in the game, and with their grass bias, just add enough Marsh near their capital (or even in their region) to reach the desired amount. This wouldn't be any less work than the start bias method, although it would be a steeper challenge -- but it would have better results. The start bias doesn't fiddle with the map, just decides which civs to put in which spots. Where the spots exist is determined by how the map divides, not by what biases come with the civs who are playing.
There is no example to follow, though. Fudging terrain for only one civ type would require a fully customized intervention. If anyone besides me knows enough about the map generation system to pull that off in a reasonable time frame, I would be impressed -- and wonder they haven't done more map modding and map scripting.
- Sirian