Aside from shell loops, I've also in the past used dsh which is
still packaged in Debian:
http://www.netfort.gr.jp/~dancer/software/dsh.html
<http://www.netfort.gr.jp/~dancer/software/dsh.html>
Other similar options are pdksh, public domain Korn shell. Which is
available in Debian repositories for some releases. And the dsh command
on IBM's aix unix-ish OS :-) So with NIM support :-) looking like rsh.
…but these days I also switched to using Ansible ad hoc commands and
playbooks for anything I do repeatedly. Well worth looking into.
The same can be said of the salt utility. Supported at cost by Saltstack
if necessary. But IMO not the same use-case that the OP intended. One
salt contributor some time ago was managing more than 10K servers with
it, I only had a few hundred.