Harri,
Thats why I use on my Openfietsmap not routable lines for highways with bicycle=no.
I misuse the avoidance of toll roads to force the routing to take cycle routes only.
In my scripts I retag all highways that are not part of a cycle route relation with toll=yes,
and all cycle routes with toll=no
I also "upgrade" cycleways and lower classified roads, but this comes indeed with a penalty of
slow or even impossible route calculations.