It's more or less happening out west already.
New houses aren't allowed to have wood heat as a primary source. And on certain days all woodburning is prohibited unless your primary heat source is wood. I believe wood pellets are even prohibited on 'spare the air' days.
It's only a matter of time... With laws like that no one will be able to rely on wood heat and people will be are forced to use alternative fuels. Then the gov't will come out with a new law prohibiting all wood burning. The writing is on the wall.
Please be more specific rather than making sweeping statements like "out west." This is a large area here and it is ENTIRELY dependent on the state or region that you live in, and it is highly varied.
Specifically, WA state has the strictest standards of any state by a long shot, and all OWBs are banned there outright. All other wood burning appliances sold must be WA state approved (far more restrictive than EPA II, and likely what EPA III will be). Also WA state has burn bans by regions within the state in winter months, and currently there are two levels of bans. Level one allows for burning in WA state approved appliances, and level two does not allow any burning (except where the home is only heated with wood). Most WA counties also require an OAK in any stove and fireplace built there.
In Oregon any home sold must have EPA or DEQ approved wood burning appliances. This does not include fireplaces. The OR DEQ has a large list of pre-EPA stoves that they deem burn cleaner and thus are not banned. All new stoves sold must be EPA approved, including OWBs. Oregon has regional burn bans in the Portland and Eugene metro areas, as well as isolated cities and towns, but no state bans.
Perhaps the most restrictive
region in the west is the SF Bay Area. No wood burning appliances are allowed in any new home construction in many of the SF Bay Area cities and counties. They also have local wood burning bans in winter there on days when there are air inversions. But that is limited to that specific region, and not all of California. Even in that area some cities still allow for wood burning stoves and fireplaces though. There are also burn bans in effect in many cities in the California Central Valley, but they are varied. The San Joaquin Valley (south part of the Central Valley) has a stove requirement similar to Oregon, where all wood stoves in homes that are sold must be EPA certified.
Most other western states vary by region, and most only have regional burn controls (if they have any). Boise, ID has wood burning bans to limit certain types of burning when air quality is bad. Western MT has stage 1 and stage 2 burnings bans. Some areas of NV have green, yellow and red burning restrictions, depending on air quality. AZ, CO, UT and NM have some city and county wood burning restrictions when air quality is bad, and most states require stoves to be EPA certified.
As for a general and complete wood burning ban, I do not think that will happen any time soon. It is highly regional, even where restrictions are in place. Also in most places they allow for grandfathered stoves and fireplaces, even in WA state. I owned a home in Santa Clara County, CA that had a fireplace, and it was legal to have and use it. Bans are on new home wood burning appliances and fireplaces, but existing houses may keep and use the ones that they have.