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The basis for the synchronization rule is that the BGP routes are redistributed into the IGP so that the IGP has correct forwarding information. But this is rarely used and has not been used for a long time; best practice, instead, is to ensure that all transit routers have the forwarding information they need by using a full IBGP mesh. Keeping BGP routes in BGP makes a simpler logical architecture and prevents problems in which large numbers of BGP routes redistributed into an IGP cause performance degradation or even system meltdowns.

From

Cover of Routing TCP/IP, Volume II: CCIE Professional Development, Second Edition

Note

not synchronizing BGP and IGP is to keep a separation so that BGP routes stay in BGP. But, the requirement is to then have full-mesh IBGP