In the Smritis, the temple priests are in fact considered fallen/degraded. Probably because they earn through the act of worshipping.

Manu Smriti 3.152. Physicians, temple-priests, sellers of meat, and those who subsist by shop-keeping must be avoided at sacrifices offered to the gods and to the manes.

3.180 (Food) given to a seller of Soma becomes ordure, (that given) to a physician pus and blood, but (that presented) to a temple-priest is lost, and (that given) to a usurer finds no place (in the world of the gods).

So, it is certainly not their responsibility to teach scriptures.

In the Smritis, the temple priests are in fact considered fallen/degraded. Probably because they earn through the act of worshipping.

Manu Smriti 3.152. Physicians, temple-priests, sellers of meat, and those who subsist by shop-keeping must be avoided at sacrifices offered to the gods and to the manes.

3.180 (Food) given to a seller of Soma becomes ordure, (that given) to a physician pus and blood, but (that presented) to a temple-priest is lost, and (that given) to a usurer finds no place (in the world of the gods).

Alternate translation from Wisdomlib.org:

सोमविक्रयिणे विष्ठा भिषजे पूयशोणितम् ।
नष्टं देवलके दत्तमप्रतिष्ठं तु वार्धुषौ ॥ १८० ॥

somavikrayiṇe viṣṭhā bhiṣaje pūyaśoṇitam |
naṣṭaṃ devalake dattamapratiṣṭhaṃ tu vārdhuṣau || 180 ||

What is given to the Soma-seller becomes ordure; to the physician, pus and blood; that to the temple-attendant becomes lost; and that to the usurer has no place.—(180)

The link also gives a similar verse from Mahabharata which is as follows:

Mahābhārata (13.90, 13, 14).—‘What is given to the Soma-seller and to the physician becomes pus and blood; what is given to the temple-servant perishes; it is neither here nor there.’

So, it is certainly not their responsibility to teach scriptures.