After uninstalling modules using Composer and removing all trace of them, Magento is still looking for them via ModuleList\Loader->getModuleConfigs()
My boss says the servers need to be restarted at least weekly
I strongly disagree. Microsoft has made great strides since the good-ole [NT, anyone?] days with regard to stability and uptime. It's a shame the consensus within IT support has not changed along with this.
How often does everyone restart their Windows servers?
Only when required -- Either because of an OS/software update, a critical software failure which cannot be recovered via other methods, hardware upgrade/replacement or other activity that cannot happen without a restart.1
Is there an industry standard or recommendation?
I have never seen a standard recommendation, per se, but I could not agree with any recommendation [except from MS themselves] which would indicate a required reboot at a specific time interval "just-because".
Is our IT department correct in saying that because we re-start that's why we're having hardware issues?
Restarting [and, more so, power cycling] is the most stressful period of hardware activity for a computer. You have most everything spinning up to 100% -- disk and fans... ...as well as significant fluctuations in component temperatures. Modern hardware is incredibly resilient, but that shouldn't be a reason for just bouncing servers, on a whim, a few times a week.
1 Aside, I loathe when techs "just" reboot a Windows server in the case of a failed service, or the like. I understand the need to get the service running again, but a reboot should be the last step in trouble shooting a server. Identifying, and fixing[!], the root cause of failure should almost never result in "Meh, just reboot it...."
Windows servers need to be rebooted monthly, if you're applying patches. You are applying patches, right? Right?
I'll give an alternative answer for a very specific case. The advances of the last 2-3 years may have changed this, but if you have heavily-used TS or Citrix servers that run a lot of interactive application (like Office), it's been a good idea to do weekly reboots off-hours, just to start from a clean slate for resources like stuck sessions, used desktop heap, etc. If you have your farm set up right and stagger the reboots, even if you have light use off-hours, users should not be impacted.
Sure, it's regular reboots of servers, but they're being used like desktops.