Hawt continues the Semitic pharyngeal fricative, the consonant behind the Hebrew cheth, the Syriac heth and the Arabic letter transcribed as h with a dot beneath it. Of the three letters in the fidel that a modern Amharic reader sounds as a plain h, this is the middle one, and its classical value is the best secured of the three, because the sound is still made in Arabic and in Tigrinya.
That second point should be separated from the general statement that Ge'ez has merged its h letters, because the merger is not uniform across the region. Amharic has lost the pharyngeals entirely, so an Amharic speaker reading the liturgy sounds hoy, hawt and harm alike. Tigrinya, spoken in Eritrea and in Tigray, keeps the pharyngeal distinct, so a Tigrinya reader makes a difference at this letter that an Amharic reader does not. The written form is identical in both cases. What differs is the reading tradition brought to it, and a description of the script that reports only the Amharic outcome misses half of its living use.
Comparative work of the kind Edward Ullendorff set out for the Ethiopian Semitic languages reconstructs the classical values from exactly this unevenness. A sound kept in one daughter language and lost in another is stronger evidence than a sound lost in all of them.