Happy to be corrected here but it's not intuitive to me that dealing with timezones as the 'base unit' makes anything easier.
For example, imagine I schedule a dentist appointment for 9AM in my local timezone sometime next summer, and put it in my calendar. Now, if the government decides that we won't do daylight saving times next year, my dentist and I still expect that appointment to happen at 9AM local time. However, if my calendar application had converted it to UTC using the timezone definitions at the moment I created the appointment, it would show in my calendar at 8AM, and I'd be an hour early!
This is not an as hypothetical situation as it seems. To give just two recent examples: the Chilean government decided to postpone the start of DST with less than a month's notice last year, and Morocco shifts the clock an hour during Ramadan, the date of which only becomes certain on the day itself.
I've been in each camp at one time or another, since being db-agnostic makes sense in some cases (libraries, products) and not in others (websites, services).