What's strange is that until I joined RPF around a year ago I hadn't thought much about props being a thing.
Oh sure I knew about props in films!
And my props were like that; they were items needed to compliment/complete a costume.
So yes my replica props fulfill the same function for which the originals had been created.
Displaying those props never occurred to me. When not being worn/carried at a Con they're in their bin. I have a big plastic bin for each of my cosplays, and I put everything related to that cosplay in its dedicated bin. When I travel to a Con I put the bin for that day's costume in the boot, which prevents me from forgetting anything! I live in dread of forgetting something- the last thing I would want is to leave a critical prop sitting on a shelf as I drive off to a Con!
In short I'm a Cosplayer not a collector.
I'm the same with music. I've worked 40 years as a professional musician, and my instruments are my tools. I have the tools I need for the jobs I get hired to do, and nothing more. My instruments sit in their cases when not being played.
It would never occur to me to
1) display my instruments, or
2) collect instruments (that is, to have instruments surplus to requirements).