For one, there is no permutation of the multiverse where after abolishing time zones people keep the cancer that is DST.

For two, nobody today just randomly calls other people they are familiar with during arbitrary hours dictated by social normative time frames without expecting conflict. You "thinking" I'll be available from 6 to 10 local time every night does not account for individual behavior. Some people do work night shift. Some people get up earlier, or later, or they go out at night. You can always call people at inopportune times, and it takes personal familiarity with someone to understand their personal time in the first place.

Additionally, you need a conversion right now to call someone on the other side of the world. That conversion is from your current time zone to theirs. It would be obviously expected people in post-TZ world would do the same calculation for unknown points of contact - plug in their longitude and yours and the difference is the hourly offset from your "daylight hours" on average.

Time zones, as they exist, are wholly arbitrary and do not accurately reflect universal daylight hours globally to begin with. You are as often wrong as you are right when you assume their time zone correlates to your waking hours and culturally normative scheduling because the time zones themselves remain arbitrary.

In the real world, post TZ, people would regularly communicate the best times to call you. You know, like you already do now. And for those you are unfamiliar with, you do the same calculations anyway - you find the difference in daylight hours between you both to find the difference in expected scheduling. That never changes, and if anything the math required is less obfuscated without time zones because you don't have all the edge cases when the time zone lines fail to accurately represent daylight hours (as is the case in all the DST conflicts between countries and time zones that obey it or not).