DNS updates are slow. BGP can react to a downed link in <1 sec.

I have both my own multihomed ASN and operate my own nameservers. The latter has usually been about as fast for failover overall in practice. BGP may look to converge near instantly from your 2-3 peer outbound perspective but the inbound convergence from the 100k networks on the rest of the internet is much slower and has a long tail very akin to trying to set your DNS TTL to 0 and having the rest of the internet decide to do it slower for cache/churn reasons anyways.