Mainframes themselves are extremely reliable. When configured as a cluster they get five nines. I'd say a power or communications failure is much more likely than mainframe downtime.

With cloud you can rely on more datacenters and, if your application is built right, it may end up being more resilient than what a mainframe setup would give you.

Downtime is a fuzzy thing. Whenever possible, I design my apps for graceful degradation - if the database becomes read-only, we can still operate in degraded mode. If we lose queues, some things will not work, but others will continue normally and many users will be completely oblivious to the alarm bells at the NOC (just kidding, there's no such thing). My SLA for full operation is much more relaxed than for degraded operation.

I think a lot of sites would benefit from offline-first and cache a bit of information, perhaps encrypted with the same password you used. There is a lot you can still do if you can a functioning site (served from a service worker) with some cached data.

You could read HN articles you read before, for example!

Not to rely on this for the nines, but as a nice way to keep things useful when there is an outage or just slowness.