I have trpuble singing A2. It is hard. The thing is: some sing-along books actually have melodies with A2. This seems strange to me since some of us aren't baritones at all. My question would be: Is it real vocal science to say that most men can sing A2? Or are there any other reasons why we would find A2 in melody books? I always thought I was a bad sibger for not reaching this note.
The typical baritone low note is an E♭2. So A2 is half an octave higher. The typical range for mixed choir tenors tends not to go lower than B2. So your melody book is aiming a bit low here, and I think the situation is even worse for females since A3 certainly is not a note expected from a soprano.
Transposing one note up adds two sharps to the key signature. Maybe the book is aiming to keep key signatures reasonably simple for the involved singers/instruments. Or the melody just has a range that cannot really be made to accommodate every type of singer.
"most singers" and "all singers" are different classifications. Considering the dearth of actual "true" tenors (in choral situations, the majority are actually baritones stretching into the tenor range), I would actually guess that at least the majority of adult male singers would actually reach that note, though not necessarily well.
My composition teacher recommended that the range for an average vocal solo not be greater than 10th or 11th. (Advanced singers can often handle a greater range.) If the range of the melodies you are talking about goes beyond this, they are probably be too hard for most singers. But if they lie within this interval range, transposing them up should work. Double check the highest note as well to see if transposing up will put you beyond your upper range limit.