Are you referring to Carcassi's Op. 60? If you are, I think one reason it might suggest playing it there is because study No. 1 from that set is marked to be played "Staccato"
, which is often easier to do on fretted notes than on open strings. The same is true of things like vibrato (only works on fretted notes) and harmonics (much easier on open strings). Things like slides and slurs require notes to be on the same string etc.
Apart from that, fretted notes do generally sound different from open strings, and it could sound a bit inconsistent sticking an open string in the middle of a bunch of fretted notes. Likewise, the same note fretted on two different strings will also sound different, and certain options may work better.
Many times, the written fingerings are just there to suggest the easiest way of playing a particular passage. There is some subtlety to this, as the easiest fingering "in isolation", might not make sense with what comes before or after a particular passage.
Either way, the written fingerings are not necessarily to be followed slavishly; if you find a way that feels more comfortable/sounds better to you then there's nothing "wrong" with doing it your way. Often there isn't an obviously "correct" choice so you'll have to try it a few different ways and make some sort of compromise between, what feels good, what works best in context and what sounds the best. Try it different ways and see what seems most sensible to you.
As to your second question, it depends a lot on the musical context. If you're staying in the same position on the fingerboard for most or all of a piece, I'd probably try to stick to playing it in the same place, unless it would make some parts very awkward. If you're shifting around a lot, then it obviously makes more sense to grab the notes wherever they are closest.
Also, if you are indeed talking about Op. 60, those aren't arpeggios at the beginning of No. 1; an arpeggio means playing the notes of a chord separately, but the notes in the first few measures don't come from a chord. What you are playing there are just descending scales, although there are some arpeggios later in the piece.