A website is just like any other software product, any change need to go through QA stage first, no matter how trivial it might seem. This is why you should always test all updates on a staging/dev server before pushing it to production.
As always it comes down to a question of ROI. Simple blogs can suffer down time for days while a fix is being work on, while sites that generate 1000$/hour probably less tolerant to hiccups, and the time invested in proper QA to avoid it is totally worth it.
So it is your judgment call in the end of how bad will it be for you if an update will break you site. If you value your time in lets say 40$/hr and the site generates 5$/hr, it is just not worth it for you to have a 3 hours QA cycle on the bi-monthly update release (not official but this is the real life rate), especially if you don’t have any bad hacks in your code and it should in theory be “future prof”