That’s not a date-time though. You would not store that using the same type-compatible objects as your regular date-times or that’s how you end up one day blowing up a Mars Orbiter.
Yes, you need both zoned and zoneless versions of dates and times. This is why e.g. java.time has both (and it has LocalDateTime for when you need to say Santa delivers presents at 00:00 on December 25).
Zoneless time is not a mistake. Using it when you meant to use a zoned time is.
Making it easier to use zoneless over zoned is a mistake, though. An even more grave one is making zoneless the default. Unfortunately, that's a mistake that we've made decades ago, and now we have to fix it in a way that deals with all the accumulated mess.
Really, though, this is a recurring lesson in software engineering: don't be in a rush to make something a default just because it's "obvious"; explicit is better than implicit. Strings are another example; we've treated them as arrays of characters for so long that it's still a common default semantics for indexing a string, except now what you often get instead is UTF-8 or UTF-16 code units rather than actual code points. All of which is likely not what you actually need - but what you do need depends so much on the task that it should always be explicit.