Even placing my mistrust aside, it's once again a US-centric move; as garbage as Apple Maps is, it's even worse outside the US.
The only reason for this choice that makes any sense, is that they've received a monetary incentive for this, and neither company has been open about it.
OSM Data/Routing engines alone don't address that side of the problem.
If I had the time, I'd personally focus on writing a loader replacement (ie, imposm/osm2pgsql "competitor") that:
1. supported arbitrary data transforms into postgres -- basically, can load data into any database schema, do on-load data transforms, enrichment, i18n, etc.
2. was distributable via some distributed message queue (I'd personally choose SQS, but you could do something like celery for less-opinionated solution)
3. was not opinionated about deployment compute environment (ie, neither requiring nor forbidding containerization)
Basically, the ability to have a proper, production-grade, not-just-meant-for-slippymaps ETL pipeline on OSM data would be a really big deal. I haven't ever seen an open source solution for that.
This is all conjecture obviously, it's hard to know exactly how much data Apple is getting, and if they could use something else to fingerprint users, but I'll give DDG the benefit of doubt for now.
Hypothetically, DDG could guard against Apple having useful navigational histories for your home by seeding requests with misinformation -- artificial navigation requests Apple can't tell apart from your real requests -- but I'd be surprised if this hypothetical is actually happening.
> like our embedded maps, powered by Apple's MapKit JS framework
The JavaScript framework they use is not necessarily the same as the server-side routing engine. One can overlay data (like the path to drive and turns to take) with any mapping library like google, leaflet, etc.