I see 2 risks:
1. Mistakes. Since nobody should access the private key, nobody knows if a mistake has been made. If so, it will be impossible to create the private key that belongs to the address.
2. You can't check if Person B gave the correct address, unless you redeem the coin. Once in a while someone would have to peel a coin to verify they're not unfunded.
One more thing: you rely on A and B not keeping and later combining those private key halves. Back to the 'trusted person' issue that we have had with Coldkey et al. Many of those creators were highly trusted and yet still they rug pulled their customers.