Just a quick correction if I may:
This is incorrect, SimBrief does update NAT tracks, NOTAMs, and weather on a regular basis (every few minutes actually), without the need for any subscription fee. This information is all freely available on the internet after all.
It should be noted that there is no absolute requirement to file a NAT track when crossing the Atlantic. Just like real world airlines, you will occasionally see SimBrief propose an off-track routing (officially referred to as a Random Route) defined as a sequence of custom lat/long waypoints (for example, TUDEP 52N050W 53N040W 54N030W 55N020W VENER KOKIB)
As far as routes go, SimBrief does try to use FlightAware routes whenever possible. Generally, this tends to give the best results as FlightAware routes are sourced from the real world and therefore should comply with any restrictions and preferential routings. Lately, there has been an increase in routes that begin with either a PBD (Place/Bearing/Distance) waypoint or a custom Lat/Long. I don't know why FlightAware has started altering routes like this, but Marc's theory on vectoring sounds logical. I'm going to look into identifying, filtering, or correcting these routes prior to including them in SimBrief.
I'd like to also note that you can always select one of the other Suggested Routes on SimBrief if you don't like the default route it proposes. Generally there are up to 5 different route suggestions you can choose from. You can also generate your own custom route from scratch by using the "Route Finder" tool on the Dispatch Options page, which gives options to enable, disable, or force a specific NAT track depending on your preferences.
Hope this helps!