We do have resiliency - the internet reroutes around these cuts l. Knock out every Atlantic cable and traffic from NY to London would route via LA and singapore.

I see this all the time on traffic from far east to Europe when a Red Sea cable dies, and I’ve seen it from India to Europe too (and seen traffic rerouted via South Africa and up the west coast a fair bit)

Latency is higher, but on the whole things continue to work. Until there’s enough damage - problems tend to be if you cut enough that cables and the routers they are connected to start to bottleneck.