To understand the benefits of welt construction in shoes you need to understand a bit of the background involved in its evolution.
Back when all shoes were handmade (before the industrial revolution of the 1800's) the cost of shoes or boots of quality was quite high. The only way to make the investment reasonable was to keep replacing the soles as they wore through, which of course happened quite often since normally you walked to get where you were going.
For flexible comfort one prefers a supple leather upper, but for durability in holding a stitched-on sole the desired characteristics are strength and firmness; repeated stitching of soles directly to the softer upper leather of a shoe would soon render the leather both unstitchable and unrepairable. When a strip of firm leather (the welting) was stitched to the flexible upper leather, and then the sole was stitched to this welting, a superior combination of materials was created. Quite simply, welt construction provided a stronger, renewable attach point for soles.
Over time the methods of constructing a welted shoe improved, giving other benefits as well. Properly made, a welt gives superior lateral stability over any other method. This is really important in helping the joints of the ankles and knees remain in proper alignment. The strength of a welt construction is also superior in maintaining the proper balancing and support of the foot. You can feel that improvement up the backs of your legs and in your lower back. In combination with the excellent fit and support of Alden's lasts, the Goodyear welt construction is far superior to any other shoemaking method for long term wear and comfort.