You're noticing that melodies usually map themselves onto the A and E strings. This is an artifact of the notes being played a certain way in isolation, and it's also a very guitar-like way of thinking about scales. In fact, it's fairly simple to play the same scales using high frets on the ukulele's C and G strings: Try a major scale starting on F4. You can play the first two notes on the C string, the next two on the E string, then G string, and the last two notes on the A string. This isn't the only way to play that scale, and you should be aware that there are many options for any major scale and any melody, each bringing a different tone to the sound.
The C string in particular finds lots of play in ukulele music, due to the fact that it's the lowest-pitched string and tends to do the best job of filling the "bass" part of the song. Many melodies that drop suddenly downwards will find themselves hitting the C string to avoid a wild position shift. Lots of common 3-note triads exist between the C, E, and A strings, especially up high on the fretboard. Even up on higher frets, it's still the lowest note in just about every chord that doesn't use open strings. The high frets on the C string are hardly useless!
The G string in particular is a string that I would partially agree with you on: its higher frets tend to go unused when I play, particularly to carry the melody. It is harder to reach, it's not the highest string, it doesn't combine as easily with the E string, and almost anything playable on the G string can be played more efficiently with the A string. That said, the higher frets on the G string are still important to the instrument in chords. Any 4-note chord on ukulele will require the use of the G-string, and when you play on the high frets, every string uses their full range.
One other time that the G-string sees utility is in playing in a "let ring out" sort of style. Taking advantage of the fact that the G string is so close in pitch to the A and E string, if you fret melody notes really close together (as if it were one unusual chord) and hold them out, you can get a similar effect to a piano's sustain pedal. This technique actually does require the use of the G-string.
Also: if intonation will be an issue anywhere, it tends to suffer on ukuleles in their high frets on the low strings, in my experience. Often if there's a choice between playing a note on the C-string and playing it on the E or G string, I will tend to favour the higher strings. This isn't universally true, but it's something to consider nonetheless.
