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.

The bigger problem, and where BGP multihoming is most handy, is it's just so much easier to get a holistic in+out failover where nothing really changes vs in DNS where it's more about getting the future inbound stuff to change where it goes. E.g. it's a pain to break an active session because the address had to change, even if DNS can update where the new service is quickly.

The long tail of routers receiving your update doesn’t matter. Once the common transit networks get it, that’s where the rest would dump the traffic to reach you anyway. The only time slow propagation to the edges matters is the first time announcing a prefix after it has been fully withdrawn.

Using the wrong route to get the packet in your general direction still gets you the packet as long as it hits an ISP along the way that got the update.

We could fully drain traffic from a transit provider in <60s with a withdrawal with all of the major providers you get at the internet exchanges. If you weren’t seeing that your upstream ISPs may have penalized you for flapping too much and put in explicit delays.