Tonsillectomy is indicated in several scenarios, including
1. Enlarged tonsils with obstructed airways
2. Sleep disorders like obstructive sleep apnoea deemed secondary to enlarged tonsils
3. One-sided tonsillar enlargement where there is a concern of cancer
4. Other less absolute indications, including recurrent tonsillitis (≥3 to 5 times a year) or resulting complications like peritonsillar abscesses
There is no real issue with removing them (ie you can live without them), but surgery entails some risks that will be explained to you by your surgeon if you are to undergo the procedure.
Hope this helps.
Cheers,
Shane