1950s Sci-Fi Style Computers, Powered by a Z80, Built in Holland

Consider the time. A 'server' usually meant 'shared file and print', not so much applications (or at least limited ones). And the disks were a couple of orders of magnitude slower than they are now. So you had a lot less overhead and could heavily optimize for smaller numbers of use cases (which made Novell very successful for a good while, tho not on z80). Also, networks were a lot slower. Ethernet had just been introduced and hadn't taken over the world. Most nets were some sort of serial network (< ~1Mbps) or maybe Arcnet (~2.5Mbps). So, yeah...there were Z80 servers. MP/M was a common operating system for them, but as we see it wasn't the only one.

There was a multiuser version of CP/M, so why not?

https://en.wikipedia.org/wiki/MP/M

That depends a lot on what you want to use it for. A Z80 can stream data to/from RAM at several hundred kilobytes a second, do binary search at tens of kilobytes per second, or calculate hundreds of floating point values a second with a softfloat library.

For basic word processing on a terminal, that is fast enough to support potentially dozens of simultaneous users. There were a number of software packages in the 1980s that would run a virtual machine interpreter, providing a multitasking multiuser environment with integrated high level languages, databases, office applications, etc. on 8-bit microprocessor hardware. Also plenty fast for a print server or similar, at that time. But, on the other hand, the 64 KB address space isn't really enough to fit even a basic optimizing compiler.

No, not high end by any means, but when running some basic business software (think rudimentary CRM, inventory management and spread sheets), quite possibly written in BASIC, chances are the floppy disks, daisy wheel printer and (few) attached 9600bps terminals would be the bottleneck.

Those things didn't compete with a Cray, they competed with a filing cabinet, desk top calculator and typewriter.

Depends on how much the Z-80 is doing. You can go the C-64/Atari way where the filesystem is running on the disk drive and the main CPU just runs the applications.

Never underestimate the obsession Europeans had with the Z80.

Someone should.

It's very jet age/high modernism, which suggests a kind of late 1950s-early 1960s vibe. Like you'd expect these in the Eero Saarinen TWA terminal at JFK.