CLAP plugins are "native" - they run on the CPU, not on the DSP of specialized hardware, so the "sound card" should be irrelevant.
I'm on a Mac, so the concept of a "C:" drive is kind of irrelevant, but I can still point out some benefits to customizing this.
For one thing, many Macs now have internal SSDs that are not user-replaceable/upgradable. If the drive fills up, it is easy enough to move data to an external drive, but what if it fills up with applications? Plugins?
While it is obviously much more important for *most* users to be able to move *samples* to an external drive than the relatively small plugins themselves, consider that temporary files and swap space all come from the main internal SSD on the Mac. Being able to install/move applications, plugins, etc. to an external drive gives power users a lot more control over how space is used on what is essentially a finite resource they might not be able to expand.
Another reason is RAID. Being able to install plugins, applications, etc. on an external RAID array can mean additional redundancy/resiliency in storing them. If the boot drive fails for some reason and needs to be replaced, install the OS and you may be good to go, or in any case there is much less to restore from a backup onto that drive. If a single drive fails in a RAID array, you replace that drive and the RAID array rebuilds it from the others, no data lost. My understanding is that newer Macs currently cannot boot from a RAID volume.
Yet another reason is portability. Buy a new computer, move the external storage to the new computer, copy over the configuration from your old home directory, and go. This takes a lot longer (to get things installed, etc.) if you have everything installed onto a boot drive that might not make the transition to the new computer along with the external or secondary drive(s).