I'm not sure how you prove that ext4 is less likely to become corrupt. But it is easily shown that it's less likely to inform you that there's corruption.

Quite a lot of the assumptions of earlier file systems is the hardware either returns correctness, or reports a problem e.g. uncorrectable read error or media error. That's been shown to be untrue even with enterprise class hardware, largely by the ZFS developers, hence why it exists. And also why ZFS has had quite a lot less "bad press" where Btrfs wasn't developed in a kind of skunkworks, it was developed out in the open where quite a lot of early users were using it with ordinary every day hardware.

And as it turns out, we see most hardware by make/model doing mostly the right things, a small number of make/models, making up a significant minority of usage volume, don't do the right things. Hence, Btrfs has always had full checksumming of data and metadata. Both XFS and ext4 were running into the same kinds of problems Btrfs (and ZFS before it) revealed - torn writes, misdirected writes, bit rot, memory bit flips, and even SSD's exhibit prefail behavior by returning either zeros or garbage instead of data (or metadata). XFS and ext4 subsequently added metadata checksums, which further reinforced the understanding that devices sometimes do the wrong thing and also lie about it.

It is true that overwriting filesystems have a better chance of repairing metadata inconsistencies. A big reason why is locality. They have fixed locations on disk for different kinds of metadata, thus a lot of correct assumptions can be made about what should be in that location. Btrfs doesn't have that at all, it has very few fixed locations for metadata (pretty much just the super blocks). Since no assumptions can be made about what's been found in metadata areas, it's harder to fix.

So the strategy is different with Btrfs (and probably ZFS too since it has a fairly nascent fsck even compared to Btrfs's) - cheap and fast replication of data via snapshots and send/receive, which requires no deep traversal of either the source or destination. And equally cheap and fast restore (backwards replication) using the same method. Conversely, conventional backup and restore are meaningfully different when reversing, so you have to test both the backup and restore to really understand if your backup method is reliable. That's going to be your disaster go to rather than trying to fix them. Fixing is almost certainly going to take much longer than restoring. If you don't have current backups, at least Btrfs now has various rescue mount options to make the file system more tolerant of broken file systems, but as a consequence you also have to mount read-only. Pretty good chance you can still get your data out, even if it's inconvenient to have to wipe the file system and create a new one. It'll still be faster than mucking with repair.

Also, Btrfs since kernel 5.3 has both read time and write time tree checkers, that verify certain trees for consistency, not just blindly accepting checksums. Various problems are exposed and stopped before they can cause worse problems, and even helps find memory bitflips and btrfs bugs. Btrfs doesn't just complain about hardware related issues, it'll rat itself out if it's to blame for the problem - which at this point isn't happening any more often than ext4 or XFS in very large deployments (millions of instances).