Such connections are called links/connectors and are needed, especially in Quebec, since we map sidewalks with the tag bicycle=no, because it is the law in the province, contrary to almost anywhere else in the world. For this reason, the router will never have access to a lot of parks because bicycle=no should stop the router to use sidewalks to access parks without a proper cycleway in them. Thus we need the links/connectors so someone wanting to go to a park must be able to reach it, even if there is a kerb. Instead of deleting it, you can change the bicycle=yes tag to bicycle=dismount so we know we should dismount because of kerbs. You mentioned "tagging for the router" with a link to the wiki. In the wiki page, none of the examples concerns this kind of links/connectors, which is documented here: https://wiki.openstreetmap.org/wiki/Tag:footway%3Dlink
The reason why this tag (footway=link or cycleway=link) was not used instead of a crossing is that it is still not available in most routing engines, but when that will be the case, we will update them in the Montreal area.
Thanks!