I think some of the dispute comes from terminology. "Line reactor" is simply a series inductor and can be placed upstream or downstream from a drive. Purposes to doing so are independent and different.
Some have chosen to call reactors ahead of drives line reactors and those in the motor lead, load reactors. I'm ok with either, it really doesn't matter.
What does matter is understanding how to use them. As far as input side reactors go, their primary purpose is the provide high frequency isolation between the drive and the power supply. Most of the time, you are trying to protect the rest of the power network from the harmonics the drive generates backward into the supply network. Less frequently, they are used to protect the drive from pulses and noise in the AC supply.
Some drive manufacturers provide some input reactance standard in their drives. I usually see 3%. Of course, the motive for not having any standard is cost and you can draw your own conclusions there!
On the other hand, load reactors are placed in the motor leads primarily to block high frequency components in the drive output pulses from traveling down the leads and causing motor insulation failures. Note that load reactors are pretty much only used to protect motors, not drives. If you have a motor rated Class F insulation, and better, meets the testing requirements of IEEE MG1 Part 31 which is a 1600V withstand test, then you will not need load reactors for most applications. In general, the longer the motor leads, and the higher the output carrier frequency from the drive increases the chance you'll need a load reactor.
In my experience, I end up needing to add input reactance about 10% of the time and motor lead reactance only about 1% of the time. (The input reactance figure of 10% is somewhat lower for me because I'm almost always dealing with a brand of drives that have a 3% input reactor included standard).
Just a couple of notes about motor lead reactors: First, they are almost never used in 230V applications and almost always in 575V. Second, on precision sensorless vector drives, motor lead reactors can damage the ability of the drive to manage motor torque slightly. And, on input side reactors, the old rule about if a little is good a lot must be better definitely does NOT apply. Input reactors drop AC voltage and, in systems that are already on the low side, they can cause low voltage problems. In those cases, you may have to pony up to a wave trap or other more elegant (expensive) solution. A comment was made earlier about an input transformer which is an expensive option in higher horsepowers. They do work good and, if equipt with taps, can even correct for low voltage. They also have the added benefit of helping reduce common mode noise which is getting to be a bigger and bigger problem, it seems to me.