No, it doesn't. Money, perhaps more than anything else in human society, exhibits network effects that incline it toward winner-takes-all dynamics. Every money implicitly competes against every other money.
I recommend taking a look at something like https://bitcointreasuries.org/
And don't just glance at it - try asking some probing questions, like "What does this mean?" and "What might I be missing concerning the underlying dynamic at play?"
You can also try reading The Bitcoin Standard for a good analysis of the dynamics and history of competition between different forms of money - the central thesis being: History has shown that you can't protect yourself from someone else holding money that's harder (better) than yours. Bitcoin is better money than anything else we have or have ever had.