A train schedule leaving London and going to Paris, Cologne, Berlin, Warsaw, Kiev, Moscow, Yekaterinburg, Novosibirsk, etc. would be difficult to plan without [time zones]

I don’t see that. If you know it takes the train 90 minutes to go between London and Paris, another 2 hours to Berlin, and a further 3 hours to Moscow, what difference does the presence or absence of time zones make in terms of scheduling that service?

You keep talking about “safely” running these programs. What is the threat that you are trying to protect yourself against? Are you concerned that your unofficial copy of the program may contain malware, are you worried that the copyright owners may try to find you (via IP address perhaps?) and prosecute, or what.