The powerful enough computer doesn't exist, and will not exist for some time. And even if it exists, it can't query the web server fast enough to have meaningful effectiveness.
So, for all intents and purposes, it's impossible. Period.
It's not security through obscurity in this case. The filenames can't be obtained or guessed through brute force. At least not with current technology or processing power...
Security through obscurity is when you hide implementation details.
Saying that my suggestion is security through obscurity is the same as telling that ASLR is security through obscurity...
People tend to conservadorism as they age, due to cognitive decline and loss of plasticity of the brain. It's a global phenomenon and usually make them make bad decisions in regards to what's best for the public or public interest.
That's why I think there must be age limit to occupy public lidership roles.
Phones can be taken. It's less improbable to the shoes to be taken.