This is an old-fashioned vocal notation practice. From the looks of it, the music in the question seems old enough to have been written in the traditional style.
Current musical notation standard practice uses beaming to indicate groupings of subdivisions of the beat; in a 4/4 time signature, eighth notes get beamed together in those groupings to visually demonstrate the location of the four quarter note beats in the measure.
This older style of notation for singers has beaming conventions as well. Traditionally, only notes sung on the same syllable would be beamed together. This ostensibly makes it easier to organize the syllables and notes together at sight. In the two examples in question, it happens that no two consecutive eighth notes are sung on the same syllable. This gives it the appearance that no beams are in use, when in fact beaming rules are being applied albeit to no effect.
Other differences from contemporary music notation include the doubling of note values (I would guess it to be sung at a jaunty tempo?): assuming the song is sung around the same speed I'm imagining it to be, I would expect modern notation to write those quarter notes as eighth notes. It seems a bit out-of-touch to have quarter note values represent that kind of vocal melody in the modern style, especially marked "Moderato". In the style this sheet music embodies, it is correct, but this seems dated to me.
As for why this was done? Some shallow research declares that "Ridin' Down the Canyon (When the Desert Sun Goes Down)" was published in 1941, and "When It's Springtime in the Rockies" was first released in the late 1920s (Autry's version out in 1937). These songs are 80 years old by now, and it would not surprise me if the older style of vocal notation was still in some prevalence at the time of writing. Especially so given the genre - country/western music tends to thematically embrace older times, so even if the old style was no longer the most common, I could see a writer/publisher choosing this notation convention out of respect for the history of that kind of music.