A high tracheostomy may be indicated in-
“It is important (in tracheostomy) to refrain from causing any damage in the region of cricoid cartilage.
An exception to this rule is when a patient has laryngeal malignancy and under these circumstances tracheostomy should be placed high so as to allow resection of tracheostomy site at the time of laryngectomy”. 
“ The high tracheostomy is generally avoided because of the postoperative risk of peri-chondritis of the cricoid cartilage and subglottic stenosis. In cases of carcinoma larynx with stridor when total laryn-gectomy would be done, high tracheostomy is indicated.”
Scleroma of the larynx
Multiple papillomatosis of larynx
Bilateral vocal cord paralysis
Carcinoma of larynx