How often are you needing to change partition geometry after install, on a server?
My short answer is "Not frequently, but when I do, I'd be very angry about having to screw around repartitioning a disk instead of fiddling with an LV, VG, or some PVs.".
I use LVM on all my non-appliance Linux systems, [0] both servers and desktops. Given that few (no?) filesystems support online shrinking but every one that you'd use as '/' supports online growing, my strategy is to take a fairly conservative guess at how big my various subdirectories need to be and leave most of my available space unallocated. Later on, if I -say- find that I need more space in '/' or '/home', or prevent a blowup in '/var/log' from eating up all the space in '/' by putting that on a separate LV, etc, etc, it's just a few commands [1] and the job's done.
[0] ...someone else has configured the storage scheme for the appliances, and I'm not going to override their choices...
[1] ...and some data copying in the case of backing a subdirectory with a new volume...
Depends. Some customers do run a lot of "pets, not cattle" servers, and those can get a few extra hard disks if space runs out. Some security guidelines prescribe separate volumes/filesystems for e.g. /home or /var/log, so log spam doesn't kill the whole system as easily. But of course, this means that sometimes the initial sizes aren't right and you need to extend something. In those cases, which happen a few times per year, not using LVM would be a huge problem.
But even for the "frequently reinstalled cattle"-usecase, LVM has benefits, e.g. snapshots for backups, debugging and forensics.