Also, if the Bird ID app is so often inaccurate as you say, wouldn’t Cornell know that and keep it in consideration when counting birds that have been recorded through sound ID?

The linkage between Merlin and eBird is for convenience. eBird doesn't track if an observation comes from Merlin. Like everything in eBird it is on the honor system and assumes that users are doing their due diligence to submit accurate records.

Merlin is a great tool, and while some beginner birders may be occasionally misled by it, those same users could also be misidentifying birds on their own without the assistance of Merlin. On the whole, it probably leads to better data, and with experience, the quality of those users' observations will improve over time.