I think this is a really good approach to handling events that someone might invite someone else to in real life. No one really ever talks about time zone or daylight savings time when you're texting your friend about a party that's happening. It's always obvious from context.
I've been working on an end-to-end encrypted event invitation service and I chose to ignore timezones completely and just have a date picker and free-form text field for time. If users want to export the event as an ical file I just set it as an all-day event and put the time in the body of the event. It's not perfect, but it's usable enough for most people.
The one exception here is importing to Google Calendar which for some awful reason imports all day events with no time zone as 24 hour long events from 12am to 12am UTC the following day.
(I have a silly beta version of the app up at https://pinvite.app if anyone cares to try it out)