How are they not irrelevant? This is a cyclical problem browsers and OSes have dealt with many times before, and JPEGXL will hardly be the last time. It's a fundamentally challenging situation that applies to the newest image codec as much as it does to old ZIP files or hostile PDFs.
There will always be some new format with some advantage or another, but safely parsing complex user generated content just isn't trivial, so every one of these is both a cost benefit analysis on its own merits but also a chance to reflect on historical implementations, vulnerabilities, and lessons learned.
If the argument is between two new formats, how are old formats at all relevant? The issues you outlined are faced by both (or any) new format so is essentially moot in the context of this conversation.
Did I miss something? The title and article are mostly about JPEG XL. What's the "both" in this? JPEG XL is the newest and has poor support. AVIF is mentioned offhandedly in that article, but it's a little older and still doesn't have great support. WebP is even older and also has occasional issues.
The image formats past WebP offer very minor improvements but have big potentials for new zero-days. I don't think it's wrong to play it safe and/or just don't implement them.
WebP is one of the most recently added image formats, and it had zero day exploits as recently as 6 months ago.