Do we need to bridge the gap? Or, to be brutally direct: Do mainframes deserve to survive in the coming decades?
Watch this video for a pretty cool story behind IBM and EBCDIC.
There are also many features in z/OS (the flagship OS) which are not available elsewhere. Things like workload manager or instrumentation facilities.
That being said, I think that advantage has mostly gone away with modern cloud computing and its matching infrastructure.
Is this more or less useful than bunch of cheap PCs in a rack. Depends on what you want to do. The bunch of PCs model generally just accepts that there will be a few blips when (not if) something goes wrong and ensure nobody will notice. The mainframe model is even the smallest blip would be noticed so you can't have any.
Other relevant answers might include "true fault tolerance". More than half of your mainframe can be burned to a crisp, or being chewed on by a dinosaur - doesn't matter, it will keep working. The closest bad analogy I can think of...is a mainframe is like the NASA space missions of yesteryear. Every component has three or four duplicates, just waiting for a primary component to fail so they can take over. They aren't cost effective, but they are operationally effective.
For example, it seems we already achieved that with disks, once embedded controllers attached to DMA-capabled HBAs became the norm.
A similar thing seems to have happened with NICs, as well as the ability to offload higher-level protocol processing (another mainframe-like feature).
Initially, you mentioned high utilization ratio and throughput. I think the former is a red herring [1], but I'm curious about the latter. I've certainly witnessed poorer I/O throughput under virtualization, but on bare metal, throughput doesn't seem to be limited (beyond the capabilities of the bus).
[1] e.g. it doesn't matter if CPU is pegged but I/O channels are at 10% if the workload is CPU-bound and CPUs are the expensive part to scale. Or substitute memory for CPU.