Routers sending cyclists down construction:highway isn’t questionable at all. I know this from hundreds of kilometers of first-hand experience where I have cycled down a peaceful, car-free route, and if there are any road-construction personnel (instead of just parked machinery and no one around) they just wave a friendly greeting. On the group chats for long-haul cyclists, many other cyclists report riding down the same unfinished highway as preferable to the road that cars would use.

Sure, there could be some roads under construction that are truly impassable to cyclists, like where landslides have completely covered the road, or where a bridge does not actually exist at the moment. But in most cases, highway=construction is a reasonable bet for a feasible cycling route.

Highways that are under construction are impassable for motor vehicles, but they are often usable (and, indeed, very pleasant and peaceful riding) for cyclists. I believe that I have seen some bicycle routers consider https://wiki.openstreetmap.org/wiki/Tag:highway=construction, https://wiki.openstreetmap.org/wiki/Tag:construction=X to be a possible route for cyclists. A tagging https://wiki.openstreetmap.org/wiki/Tag:construction:highway=road could disrupt functionality in existing tools.

In some countries now (Poland is a good example), so many of the sidewalks are actually combined or segregated footways/cycleways. This means they have to be tagged separately using the relevant preset, so that bicycle routing is improved. Also, a sidewalk will possibly have different surface= and smoothness= values from the road that runs alongside it.

area:highway does already render in map apps in wide use like OSMAnd, and the area:highway tagging has long been considered mature already across multiple countries.

Keep in mind that the map at openstreetmap.org is just a tech demo, not a real consumer product. It lacks support for rendering many tags that have been well-established and widely used for a long time now.

You shouldn’t base your tagging choices on what produces the desired rendering on the openstreetmap.org map.