Why is a Time Machine backup so slow over a fast network?

Despite having a gigabit hardwired ethernet connection to my Macbook Air, when I have Time Machine backing up to an iMac also hardwired on the same switch in the same network, the transfer speed is often less then 1MB per second.

If/when I copy a file from the Air (Catalina 10.15.7) to my iMac (Mojave 10.14.6), I get a speed of about 65MB per second. As it is, it takes about a month to get the 1Tb disk in my Air backed up, all that time sitting there with a wired connection and doing little else. If I could get 65MB/sec with Time Machine, it would take less than 5 hours to backup that 1Tb disk.

The backup disk is a 5Tb portable USB drive connected to the server (my iMac running Mojave) and configured to "share as a Time Machine backup destination". Several Macs (High Sierra, Mojave, Catalina) are successfully (but slowly) backing up to it over WiFi.

How can I get the initial backup to go as fast as possible?

Time Machine is really poor at working over a network, and I’ve stopped doing this. The best way to run Time Machine now (macOS 11) is to give it a dedicated encrypted disk (which TM will reformat to APFS). The backups will be very fast and you will be hard pressed to notice them, but even backing up to an HFS+ local drive will be orders of magnitude faster than over your LAN.

(The reasons for this are somewhat opaque, but the backup process is very different when backing up over a network as your target is not a disk or even a network folder, but a sparse image file on the network and this makes, as you’ve seen, a huge difference. The behavior seems to have gotten worse in recent versions to the point where it’s just not worth it.)

Another option you might consider is to use a syncing tool to sync your data to a location on the target machine that is part of its regular backup. I’d do both, but then I’m a "three backups are the minimal starter set” sort of guy.