> move any partitions as required until the free space is next to the partition you want to enlarge
The only reason you find this "easier" (I clearly don't) is because GParted has a graphical interface while LVM has not (yet?).
To the best tool is quite often the one you are the most familiar with.
When repartitioning I trust nothing and no one (neither GParted nor myself). So I much prefer spending 10 minutes googling and reading the LVM man pages and eventually do something conceptually simpler and that involves 5 or 10 times fewer operations, i.e, 5 or 10 times less chances for something to break.