There is an excellent wikipedia page about the the procedure called tonsillectomy: "Although tonsillectomy is performed less frequently than in the 1950s, it remains one of the most common surgical procedures in children in the United States and many other western countries."
That WP page is amply sourced with research papers, the following box is just a shortened excerpt.
Complications
A recent study states that tonsillectomies in young children (0 to 7
years) are correlated with weight gain in the years following surgery.
The morbidity rate associated with tonsillectomy is 2% to 4% due to
post-operative bleeding; the mortality rate is 1 in 15,000, due to
bleeding, airway obstruction, or anesthesia complications.
Impact on immune system
It remains controversial whether tonsillectomy may negatively affect
the immune system. However, multiple studies have confirmed
correlation between a previous history of tonsillectomy and a wide
range of diseases, such as:
Hodgkin's disease, Non-hodgkin's lymphoma, Laryngeal cancer,
Esophageal cancer, Thyroid cancer, Breast cancer, Prostate cancer,
Base of tongue cancer, Leukemia, Asthma, Hay fever, Irritable bowel
syndrome, Crohn's disease, Appendicitis, Heart attack, Sarcoidosis,
Rheumatoid arthritis, Multiple sclerosis, Deep neck infection,
Poliomyelitis, Recurrent cellulitis, Primary biliary cholangitis,
Chronic rhinosinusitis, Pediatric autoimmune neuropsychiatric
disorders associated with streptococcal infections.
Moreover, other studies have found that tonsillectomy may lead to:
- a decrease in levels of serum immunoglobulin
- a decrease in levels of secretory Immunoglobulin A
- an increased risk of autoimmune disease
- an increase in mortality between the age of 18 and 44
- an increased risk of chronic disease
- an increase in overall cancer risk
Mark's comment is basically right:
"The simplified version is that alternative short-term treatments got
better, and long-term studies showed that the long-term benefits
mostly didn't exist. Still looking for sources."
But this is also actually a very prominent example of very widespread bad practice that once was the standard. One study shedding some light on this can be found in the historian David Wootton's "Bad Medicine: Doctors Doing Harm Since Hippocrates":
Moreover Lister’s innovations made possible new types of bad medicine.
For the first time it was possible to operate on the abdomen, and some
surgeons proceeded to happily chop out bits and pieces (an appendix
here, a colon there) not because they were infected, but because they
might one day become infected––the historian Ann Dally has called this
‘fantasy surgery’. These operations never became the norm, but
tonsillectomies did, and we now know they did more harm than good.
Worse still, the decision as to whose tonsils should be removed was
not remotely rational. Of 1,000 11-year-old children in New York in
1934, 61 per cent had had tonsillectomies.
The remaining 39 percent
were subjected to examination by a group of physicians, who selected
45 percent of these for tonsillectomy and rejected the rest. The
rejected children were re-examined by another group of physicians, who
recommended tonsillectomy for 46 per cent of those remaining after the
first examination. When the rejected children were examined a third
time, a similar percentage was selected for tonsillectomy so that
after three examinations only sixty-five children remained who had not
been recommended for tonsillectomy. These subjects were not further
examined because the supply of examining physicians ran out.
Clearly
the decision as to who should have a tonsillectomy was entirely
arbitrary. This was bad medicine alive and well in the 1930s.
First: do no harm. Since tonsillitis is still a common problem, the actual illness may be differently classified or diagnosed today. There may be other treatments available. But just cutting it out was of questionable effectiveness in the first place, could and did lead to a number of side effects and unwanted complications or long term effects. Together with the observation that most of the time not even the official guidelines were able to ensure a good practice, and many doctors were apparently unable to follow them, it is a good thing that this tonsillectomy fad is further falling out of fashion.
