The word "private" is missing in the first sentence in brackets: "in NRW a track is neither private nor public"

In general, tracks can also be used by all motor vehicles. However, that differs from state to state (in NRW a track is neither nor public, i.e. the question is not easy to answer). In most cases a sign that prohibits motor_vehicles is used.
Adding the appropiate tags (motor_vehicle=agricultural, etc.) is highly encouraged.
I understand your issue, however, I suggest to stick to common mapping patterns (primary use for agricultural traffic --> track).

Ok, I totally follow your argument regarding the cycling routers (I often use those and wonder why they don't use tracks). However, to improve the routing we could add tags describing the smothness, as this is often used by bicycle routers to determine usable roads.
My objection is that with looking on the map (e.g. slippy map on openstreetmap.org) one should be able to determine whether a way/road is accessible or not. Mapping it as a track makes it clear, that no regular motor vehicles may use this road. Leaving it as unclassified may lead to the understanding, that this is an allowed shortcut (here: between "Schierwaldenrath" and "Harzelt"). If a way is not only for agricultural traffic, I totally agree to map it as unclassified or service (depending on the usage). I love the idea of having a clear distinction between highway=unclassified/service/track, as shown in the link I provided in the first comment.
Example: The way "Holzweg" north east of this changeset is similar to the road in your changeset. However, it is NOT restricted to agricultural traffic and thus, not mapped as "highway=track".

(By the way, I live there and all people commonly refer to the way between Harzelt and Schierwaldenrath as "Feldweg" [track] ;) ).
I will try to make an update to smoothness, etc. (also for some surrounding ways) this evening.

I'm sorry but I have to disagree. Many roads that are paved (with asphalt) are tagged as highway=track due to their usage as "agricultural road". If you have a look at surrounding roads you will find a lot of ways where highway=track, tracktype=grade1 and surface=asphalt/paved. I.e., according to your logic all of those ways should be tagged as highway=unclassified. However, as those roads are only used by farmers to access their fields, they are commonly tagged as tracks (at least in Germany).
Rule of thumb: Only agricultural/forestry access: highway=track. Open to all motorized traffic: highway=unclassified/service/etc.
Please revert your changes. Thanks.
If you have more questions, feel free to PM me.

Could you please explain, why you changed the highway class to unclassified?
According to osm.wiki/DE:Tag:highway%3Dunclassified#Abgrenzung_von_highway.3Dunclassified_und_highway.3Dservice_und_highway.3Dtrack_tracktype.3Dgrade1 this way should better be mapped as a track, as it was before.