Yes, I have had /boot and /var that were on separate LVM volumes fill up due to unexpected behaviour before now, and it's irritating when that happens.
However, in neither case did I lose personal data, In the worst case, I could have re-installed the operating system and carry on with the existing /home (on its own volume). Having a single partition or volume for everything is simple and convenient, but the aberrant log-file that filled up my /var would have filled up an entire disk quite happily.
Some people advocate using LVM and not allocating all the space on the disk initially, leaving a buffer than can be used to extend any LVM volumes that fill up.
As ever with Linux, your use-case and level of experience/competence determine the optimal solution for you, and the great thing is that you can usually find a configuration that works for you. Currently my daily driver laptop has (from bottom up) a LUKS encrypted disk with only the ESP in plain-text, LVM, a swap volume, and a BTRFS volume with a subvolume for /home, and some unallocated LVM space. I will not argue that it is the best layout for anyone (including myself) as I'm experimenting with BTRFS at the moment. It hasn't cause me any immediate pain points.