I have a lot of sheet music where the singer is a baritone and sings a lot in the C3 - C4 region. This would normally be written in the bass clef but in my sheet music, the notes are written in the treble clef one octave higher. Is this because it is harder to read in the bass clef or is it so that you can have both the vocal melody and harmony in different octaves so they can be both played on the piano and notated in different clefs?
I think the simplest answer is that the treble clef has become the "default" clef for the vast majority of voices or instruments, regardless of transposition. Aside from occasional examples of the "vocal tenor clef" (with the little 8 below the clef sign), it is just assumed that a singer or instrumentalist will know to transpose to the correct pitch depending on instrument or voice part.
Forget about singers for a moment and consider the huge variety of transpositions implied in music written in treble clef. A standard B♭ trombone is non-transposing in the bass clef, but a B♭ trumpet is generally notated so that every pitch is written up a whole tone. No special marking appears on the clef.
Now you may say "But that's different! It's still in the right general range!" Okay, that's true. But consider entire families of instruments all written in treble clef, even when the pitches sound far below. B♭ clarinet follows the transposition of B♭ trumpet in treble clef. But bass clarinet (often in B♭) is transposed up a ninth in written form; same thing with tenor saxophone. Contra-alto clarinet and baritone sax are transposed up a thirteenth, still in treble clef with no indication of transposition. Contra-bass clarinet and bass saxophone are transposed up a sixteenth (over two octaves) with no indication of anything unusual in notation -- still just the standard treble clef. And this occurs even for octave transpositions, such as with notated guitar parts on treble clef (often with no explicit octave transposition indication).
There are obvious reasons and advantages to some of these traditions -- in the case of woodwinds, the advantage is preserving fingering with the notated appearance of notes on the page. Thus, this tradition of using a treble clef with no explicit indication of transposition became standard by some point in the 18th century.
The use of treble clef with no indication of transposition for tenor and baritone voices (and even occasionally with bass solo parts) follows in a similar tradition. Notated instrumental transposition became widespread by the early 1700s (almost always using the treble clef), and vocal transpositions by octave for tenor and baritone parts (written in treble clef) followed and became an option for solo parts by around 1800. By the time Schubert and Schumann were writing song cycles for tenor/baritone in the early 1800s, their manuscripts were inevitably in treble clef for the solo voice part. It was only in the late 1800s that any sort of "vocal tenor clef" appeared -- at first a doubled G clef (to indicate a transposition down by octave) or a C-clef in the third space. I believe it was only in the 20th century that the "8" designations started to be added to clefs to indicate octave transposition.
It's notable, by the way, that this transition happened roughly around the time that other vocal clefs went out of fashion. In the 1700s, it was still most common to see C-clefs for soprano clef, alto clef, and tenor clef in voice parts. Basically, the C-clefs were dropped and replaced in vocal parts by a single consistent G-clef, sometimes at pitch and sometimes transposed by octave. (Basses likely retained their clef to avoid an excess number of ledger lines.)
Meanwhile, other clefs don't have this transposition association in modern musical practice aside from a few specific cases (like string bass parts that are notated an octave higher than they sound in bass clef, again without octave indication). Unlike centuries ago when the knowledge of a wide variety of clefs -- often placed on various lines of the staff -- was expected of musicians, today the vast majority of people who can read music notation can only read one clef fluently: the G-treble, specifically located on the second line from the bottom of the staff. (I have personally known graduates with music degrees from prestigious universities who can't read other clefs except with great difficulty.)
As other comments note, vocal music is also frequently transposed by octave. Songs obviously written for female singers are sometimes sung by males and vice versa. Given the ubiquity of the treble clef for the past couple centuries, the convention for which clef to choose for maximum flexibility is obvious.
Vocal music written for the tenor voice is written in the treble clef one octave higher. Vocal music written for the baritone voice is written the same way as that for the bass voice: in the bass clef.
It might be that -- regardless of the range and quality of the voice of the singer you are writing about -- the sheet music you refer to is written for a tenor to sing.
The sheet music version is often used for instrumental arrangements, and it's easier for an arranger to read a melody in treble clef cos most of them are right handed.
Bass, tenor, and alto clefs, are used in orchestral arrangements for specific instruments.
Most opera scores indicate baritone voice parts in bass clef, although I have seen tenor clef (as in the C clef) used for both baritone, and tenor parts. An example being Wagner's "Ring Cycle".