The way I see is that the main benefit of mapping highway=* values to certain well-known/official classification is that this way we have a clear criteria on when to use certain highway=* value. 

Also roads on Maa-amet maps are given prominence/stand out based on the same classification of national roads, and so I'd expect that Estonian users are more or less familiar with this approach being applied on individual roads in OSM as well. Also this official classification after all also generally indicates which roads are actually more important.

Alternatively we might look for some other more or less clear criteria. Ideas for other as feasible criteria don't come to my mind at the moment, though. E.g. if we tied highway=* values to official traffic density data then probably it'd be considerably more difficult to main the OSM data accordingly, and likely the result wouldn't be as intuitive for end users.

People may have all sorts of reasons on why certain road should stand out, in part also depending on if they are a cyclist, or a user of certain routing service, as it comes out from your reply. I find that this way it's rather difficult to decide on which highway=* value each road should get. Should we discuss or maybe even vote on each road/road segment then? Even if we decided on it road by road, we probably still should come up with some (broad) alternative criteria first, as otherwise the road data as a whole would likely look inconsistent to end users.

I believe there is transit traffic but it isn't evident to me how this translates to highway=* values, and more specifically what degree of transit traffic should be considered highway=secondary, as said.

As for routing in particular, are you referring to some certain router? To my knowledge highway=* values are not strictly related to specific routing functionality, and also different routers work slightly differently anyway. So probably it isn't really desirable to tweak highway=* values only to get certain result in certain router. If routers generally don't work as expected then shouldn't we assume that some other more straightforward routing data is missing for particular roads?

As for visual inspection, I'm not sure I understand. It again doesn't seem evident how exactly does traffic density translate to highway=* values. As for providing information to cyclists in particular, e.g. "class:bicycle" key seems to provide that sort of information in a more straightforward manner.