Are there travel trailers built to full time in?

Some TT are not designed for year round or continuous use. That is why some manufacturers advise against it.

Full time occupancy usually requires a larger unit, hence the recommendation for 5vers and Motor Homes, but do not expect the typical TT, which is built and priced for recreational use, to hold up to continuous occupancy.

As mentioned, if you want a TT for year around use, they are out there. Their features, amenities and cost are reflective of there intended use.