If the instrument is tuned in fifths then, indeed, a diatonic scale pattern that proceeds perpendicularly across the finger board at the same position has four notes on each string.

However, these four notes are sometimes spaced differently: different patterns of tones and semitones.

When an instruent is tuned in fourths, scales use three notes. There are ways to conform to many of the string-to-string pattern variations by leaving out fingers:

   a - b c'  # index ring pinky
   e f - g   # index middle pinky
   - c - d

It seems that the fifths tuning is quite tyrannical in this regard.

Now when it comes to the major scale, that scale is actually a stack of two identical tetrachords, which are a fifth apart. These tetrachords have identical fingerings:

   # tuning in fifths now:

   g - a - b c
   c - d - e f

So now if you have your fingers spread out in the right way to play the C-F tetrachord, all you have to do is preserve that when going to the next string.

I suspect violinists must be exploiting this sort of relationship; favoring fingerings that show tetrachord symmetries.

The Dorian mode (D to D mode of C major) also has two identical, stacked tetrachords, so if we slide one position down that pattern, we are still good:

   g - a - b c - d
   c - d - e f - g
      [  Dorian box ]
  [ Ionian box ]

But, having observed that, these fingering patterns are not easy even in isolation, regardless of whether there is a change in the pattern going to another string.