All general purpose machine guns (GPMGs) that I am aware of retain the interchangeable barrel function - a GPMG being a roughly 7.62mm belt-fed platoon- or company-level machine gun capable of laying down large volumes of fire. The M240 and MG3, the most common GPMGs in the western world, certainly have changeable barrels, and soldiers are taught to do so when laying down large volumes of suppressing fire. Even the intermediate-caliber M249 Squad Automatic Weapon has a quick change barrel.

Now, there are some lighter automatic weapons that do not have a changeable barrel. But that's nothing new. The Browning Automatic Rifle, Chauchat, and Lewis Gun did not have changeable barrels. It generally doesn't become necessary to change a barrel until you've fired several hundred rounds through the gun, or less if you're firing very rapidly. Weapons that don't have quick-change barrels just aren't intended to produce the same volume of fire as a proper heavy/medium/GP machine gun.

Interchangable barrels are still very much in use.

The M2A1 Machine gun in use by the US Army has an interchangable barrel that is considered an improvement over the older screw in barrel changing mechanism as noted by the Army itself. The barrel extension also makes possible rapid barrel change-outs on the M2A1. With the older M2s, the barrels had to be screwed on. To change the barrel of an M2A1, a Soldier simply needs to slightly retract the charging handle, rotate the barrel by its carrying handle and slide the barrel off the receiver. The M249 light machine gun also requires a barrel change after a period of use. When used as a machine gun, the M249 requires a tripod, a T&E mechanism, and a spare barrel.

I have used both of these weapons, it is incredible how quickly they heat up when used even under ideal circumstances on the range. The barrels themselves can and do melt, and can become jammed very easily.