Putting aside the cruelty debate on this, there is also the issue of the flamethrower's impracticality on today's battlefields. We're looking at a mix of conventional and asymmetric warfare with the latter being more prevalent.
Looking at the conventional warfare in recent conflicts (Iraq and Afghanistan), you've got two factions fighting on the open field from dozens, hundreds of meters apart. These battles are won with the proper application of indirect fire (artillery) and direct fire (combat teams consisting of maneuvering armoured and infantry elements). The Western countries clearly have the superior firepower at range so it never really comes to the up close and personal that the flamethrower is effective at.
Now, looking at the asymmetric portion of the same recent conflicts, we're seeing a combination of guerrilla and urban warfare. The use of IEDs and their variants (VBIED, RCIED and VOIED) make the use of flamethrowers irrelevant. Also, fighting in an urban environment means there are most likely innocent civilians around. The indiscriminate use of the flamethrower could result in unacceptable and avoidable collateral damage with the ultimate loss of the initiative on the political stage and in the eyes of the public and the media.
Does that mean the flamethrower is completely useless? Not necessarily. I haven't the foggiest on how many ops ISAF is running in the mountain caves along the Afghanistan/Pakistan border. However, those seems like the only places to effectively use a flamethrower...