Depends on the lettuce. Iceberg lettuce is trash and deserves anthing you can do to it
I find it best as a vehicle for blue cheese dressing and bacon in a well-made wedge salad. Iceberg lettuce has three reasons it is a common burger choice: it's inexpensive, it offers crunch, and it's easily grown. Lettuce cups take labor to separate (working against the inexpensive benefit) and the crunch varies depending on how near the core/heart that part of the leaf is. Shredded lettuce distributes the crunch evenly, it can be done by machine, and can use more of the lettuce that otherwise wouldn't work on a burger. Iceberg's downside--it doesn't taste like anything--is more a missed opportunity than a downside for those not wanting a stronger taste like you'd get from arugula or shredded cabbage, as sixdegrees suggested.
In short, the reason you see it all the time in mass market fast food burgers is because it is easier and cheaper to get a more consistent "okay" product using purchased, bagged, shredded lettuce.
Personally, I like to take a cross section of cabbage and char it on a grill or cast iron pan in the drippings from the patty while the burgers rest for a couple minutes--just char it, not cook it all the way through--then slice it finely (aka shredded) and toss it with a little mayo, mustard, salt, and sherry vinegar for a crunchy slaw (under the burger to help the bottom bun survive to do its thing). Alternatively a slaw made from raw shredded brussels sprouts, olive oil, lemon juice, salt, maybe some grated parm is also hgreat in the same place or just as a side dish (add in some roasted pepitas or toasted almond if you want it as a side).
I cannot remember the last time I bought iceberg lettuce, to be honest. Red leaf, butter lettuce, arugula, kale, all the time--we eat salads three-four times per week.