I've tinkered with LVM2's mirror support, and I can say: It's not really meant to replace RAID1.
The real use for LVM2 mirroring is to transfer data between volumes. Say you have a drive failing, and you want to get data from point A (which is in peril) to point B (which is safe). The point of the LVM2 mirror function is to clone off the data to other parts automatically, while allowing regular I/O to proceed. After the "mirror" is caught up, you break the mirror and remount your data on the new, safe location.
The speed at which it does this is less-than-stellar. Like, worse than 50% slower than just a straight RAID1. In fact, it's so slow I can watch two drives that are part of an LVM2 mirror strobe the activity light at different times. But if you need to shift data between physical locations, it'll do the job transparently, and that's what LVM's really all about - transparent management of the storage layer while the filesystem is active. RAID is more about avoiding data loss due to a single point of hardware failure.
The issue of "overhead" really isn't there. The only real issue you'll encounter is recovery, and that's a posting unto itself. Recovering data from a blown filesystem is hard, recovering it from a three-layer filesystem (RAID/LVM/Ext4) is a PITA. So it's kinda important to make sure the drives are healthy (SMART), the array is healthy (mdadm), your volume groups are healthy (LVM2), and the filesystem is healthy (fsck). I've lived through this once, and I would rather not do it again.