The unique solution in BBR is to add "required mixin" flag to outputs.

First of all this idea doesn't provide guaranteed anonymity to sender because it only FORCES other people to use some specific level of mixin factor in future transactions. Sender and the transaction he creates aren't affected directly.

The potential problem goes from possible unspendable transactions in the blockchain: you can create an output with some very unusual amount and force addressee to spend it with big mixin factor. In case forced mixin factor is greater than number of outputs with the same amount in the blockchain this transaction will be unspendable for a long time. Addressee even will be unable to send this money back. CryptoNote protocol SHOULD NOT allow such situations.

I see a good intention here from BBR developers but this forced anonymity doesn't look like an improvement in CN protocol (at least right now) and requires additional design/development efforts. Additional checks of transactions being accepted to mempool or to block probably will do.

Here is another analysis of forced anonymity in BBR: https://forum.cryptonote.org/viewtopic.php?f=12&t=239