Most singers who can read music will have learned in the course of learning a musical instrument. Piano is the most common, and of other instruments the higher sounding ones are often preferred for students, both because they are cheaper and because there is more solo music written for them. Thus most of these singers will have some familiarity with the treble clef. On the other hand tenor clef will be familiar to relatively few singers - those who have studied cello, trombone or bassoon well past beginning level, and those who have made a point of learning to read tenor clef.
Singers reading music will often need to read from a grand staff. A separate vocal staff is not always provided; some songs are written as piano music on a grand staff, with the singer being expected to pick it out from the rest of the piano part, the words being placed between the treble and bass staves. Hymns and similar vocal works are also written using a grand staff, as this allows the four vocal parts to be written on two staves.
Singers who do not read music need to memorise their parts. This is normally done by repeated practice with the assistance of a pianist or an organist, who reads grand staff music.
Many songs are often sung by several different types of voice. With ranges roughly an octave apart, tenors and sopranos can share a lot of sheet music if the tenors read treble clef and sing it an octave lower.
To have access to all the above music a tenor needs to be able to access treble and bass clefs.
Note that the octave-transposed treble clef covers the notes D3 to G4 without ledger lines, while the tenor clef covers the range C3 to F4 without ledger lines. Either clef fits the tenor range well; there is little inherent difference in readability.
Tenor clef music may be useful in choral music written on separate staves and in music that is specifically for tenor. However, as noted above, knowledge of tenor clef is somewhat restricted. More tenors and more accompanists can read treble clef than can read tenor clef. As there are no particular advantages in using tenor clef, but there are significant advantages in using octave-transposed treble clef, the latter is now almost universally used.
Note that this discussion does not apply to instruments such as the cello, whose players must read bass, tenor, and (untransposed) treble clefs.