Technically those footpaths have nodes in OSM (see below). Footpaths generally don’t have names though and the ‘Path’ & ‘Footway’ are ignored in CS import anyway (Google Doc of types imported & further info on import process.
As to why the route builder may route onto path vs street, that’s likely because the builder is looking for ways with foot access set to yes (or other allowed options). Which makes sense because we are traveling by foot but I get what you mean since we are aiming to complete streets. I’ve found when building routes, if I do see it want to go onto a path, I’ll draw shorter spans between clicks; especially around corners I’ll make one near end of one street and just around bend to where I’m turning. From there you should be able to route straight for the rest of that block without it jumping curb onto footpath/sidewalk.
