The Trade Way itself isn't broken — WotC’s cartographers have just forgotten it’s there
The "broken" Trade Way is a symptom of the maps being drawn and redrawn too many times over the editions, and a lack of careful cartographic referencing far enough back when redrawing them. Like a game of Broken Telephone, the deterioration of the Trade Way's depiction (as opposed to its in-world state) can be traced through lapses in mapping between the editions.
Since the beginning of FR publishing, the Trade Way has been continuous between Waterdeep and Scornubel; ditto the Coast Way between Baldur's Gate and where it meets the Trade Way south of Dragonspear Castle. In the AD&D 1e and 2e maps, the Trade Way is marked in the Fields of the Dead with the line-symbol for "trail" rather than road (as the rest of the Trade Way is marked), along with numerous small tributary trails through the Fields of the Dead, and that portion of the Coast Way.
For some reason, in 3rd edition both the Trade Way and the Coast Way are marked the whole way as "road" with no "trail" sections in the Fields of the Dead, despite no corresponding change in the conditions in-world, and despite some trails being marked right beside them. However, the 3e map is not a good map. While the 1e and 2e maps closely track each other, the 3e map was notable at the time for being much prettier while grossly distorting most details of the geography of the Realms. (The Fields of the Dead in particular shrank by more than half, moving Baldur's Gate much farther north than it should be and warping the shape of the Coast Way, and the things the cartographer did to Cormyr, the Dalelands, and the rest of the original "core" lands of the Realms is enough to make a map-lover cry.)
Notably, the 4e map tracks with the 3e map, and shows the Trade and Coast Ways as fully "road" (and intact) along their whole length. That rules out 4e-era catastrophes and cataclysms as being in-world responsible for the addition of real gaps.
It turns out that the lack of these parts of the Ways on the 5e maps seems to be a fault of the cartographer going back far enough, but to the wrong maps. The first time that gaps were mapped in the Ways was actually in the 1e maps — in the continental-scale maps. These maps only marked the "road" portions of the two Ways, leaving depicting things like trails to the detailed regional maps. It is this continental-scale view of the Fields of the Dead that the 5e maps appear to be based on — even the zoomed in region around Baldur's Gate, which really should have been based on one of the regional-scale maps instead of on a continental-scale map, if the effort to reference 1e maps was being made anyway.
(Aside, the 5e map around Baldur's Gate restores the Fields of the Dead and environs to their proper size and shape. That's nice to see, though it does make it doubly confusing why the mapping lapses in the Ways at that scale weren't also corrected.)
So that's all that's going on: The 5e map just doesn't chart any routes categorised as "trails", probably because it was based on a map that didn't mark them either, so it looks like the Trade Way and Coast Way are broken. With no depiction on even the more detailed maps, it makes it seem to someone coming to the Realms for the first time in 5e like it's a deliberate break rather than just a failure to mark them. And because these maps are not being presented alongside a detailed almanac of the Realms, as the original maps were, there's little beyond the map for a reader to draw conclusions from.
The Ways are there, though. The maps are just not showing the parts of the Ways that are rougher, that are passing through the region of sparse civilisation that is the Fields of the Dead.