There's a need for a standard that locks down the commonly used variants of it and gets rid of all the ambiguity.
For me, timestamps following this pattern 'YYYY-MM-DDThh:mm:ss.xxxxxZ' is all that I use and all my APIs will accept/produce. It's nice that other legacy systems are available that don't normalize their timestamps to UTC for whatever reason, that consider seconds and fractions of a second optional, etc. But for unambiguous timestamps, all I want is this. It's fairly easy to write a parser for it. A simple regular expression will do the job. Of course add unit tests. Technically the Z is redundant information if we can all agree to normalize to UTC. Which IMHO we should. In the same way the T part and separators are redundant too. But they are nice for human readability.
You can use datetime libraries that are widely available to localize timestamps as needed in whatever way is required locally. But timestamps should get stored and transmitted in a normalized and 100% unambiguous way.
It's only when you get into supporting all the pointless and highly ambiguous but valid variants of ISO 8601 that parsing becomes a problem. There's actually no such thing as a parser that can parse all valid variants with no knowledge of which variant is being used. There are lots of libraries with complex APIs that support some or all of the major and minor variants of course. But not with just one function called parse().
I think the main challenge with ISO 8601 is that it never called out this variant as a separate thing that you should be using. This really should be its own standard. And not using that would be a mistake. ISO 8601 is what happens when you do design by committee.