Alternatively, I can just use TimeZones which does it for me, In every country of the world that I've worked with. This even accommodates daylight savings, when people come into work earlier/later at certain times of the year. And my algorithm takes all of 5 seconds per meeting - I wouldn't call it inefficient.

UTC is great for a lot of things (I was one of the people who introduced it to our NOC, ensured that on all servers, /etc/localtime -> /usr/share/zoneinfo/Etc/GMT so our log files could be easily correlated.) - but for figuring out when people around the world are available to work with you - local Time Zones do a much better job.

Also - as noted elsewhere, when I'm traveling from country to country - Having a local timezone to tell me if I'm landing in the morning/afternoon/night is invaluable. Once again - only possible with Local Timezones if you want to represent the time with a single number.