There is a considerable amount of implied physics and technology contained in the statement ‘butting increases joining strength’.
The posters in this thread have touched on many true aspects of this science but I don’t believe any one has expressed the fundamental truths behind the reasons and considerations involved in using butted tubes.
Lets look at the dynamics of the whole bike frame. As in any complex dynamic structure there are regions where flexing is allowed or may even be advantageous, and there are places where it is best that extreme stiffness be maintained. For example, controlled flexing in the fork tubes is used to great advantage, while the drive side face of the bottom bracket shell and the mounting plane of the derailleur dropout should stay parallel to each other within a very small margin, even under the most severe conditions.
The simple answer to why butted tubes are used, does as stated, lie in the reality that you need enough material at the joining point to physically make the joint survive. Even lugged joints that are brazed and supported on the outside of the tube need enough thickness at and near the joining point to resist the flexing, twisting energy that is generated in the length of the tube to insure their integrity. Beyond that, just how a joint transmits or attenuates flexing energy is the key to good design. Double butting makes gradual steps for a smoother transition of energy in some cases. How a frame accepts and returns the energy put into it determines its pedigree.
While it is true that you could just figure a tube diameter and a wall thickness required to achieve a certain amount of overall stiffness and then thicken up the ends to allow for welding etc. The truth is that in order to buy tube you must have a specific dimensional pattern that the manufacture will supply.
In most cases, manufactures pick, a top tube for example, with a thin wall section length that will be appropriate for their smallest frame. To make their larger frames they cut less and less from the butted ends to make the longer tubes. The better but more costly way is to have a specific tube with the thickness and length of the butted or double butted ends tailored exactly for the specific intended use. This can cause a frame manufacture to spec many more tubes from a tube supplier, but the end result if done properly, can be the best handling and lightest frame in every size.