An Article I found at BRASSMUSICIAN.COM
It can be argued that all music – be it Bach, Bartok, tonal, atonal, medieval, or avant garde – is made up of parts of scales and arpeggios arranged in different combinations and permutations.
But why should we practise scales and arpeggios?
Reason 1. Knowledge of a wide variety of scales and arpeggios can help us to learn new music more quickly and efficiently.
Reason 2. In the same manner, scales and arpeggios improve sight-reading and transposition ability.
Reason 3. Playing scales and arpeggios covering ranges of a 12th, or 2 full octaves, can encourage whole range practice on one embouchure. (i.e. Helps to eliminate the need for an embouchure change when passing between registers).
Reason 4. Clarity of articulation is another aspect of playing which can be greatly improved through scale and arpeggio practice.
Reason 5. Various articulation combinations can be practiced within a scale, which can help to further train co-ordination between the tongue and fingers.
Reason 6. Scales and arpeggios are naturally designed to build endurance if you rest as much as you play.
Reason 7. And finally, focussing on the purity of intervals whilst practicing scales and arpeggios greatly helps the ear to tackle intonation issues.
Can you think of even more reasons to practise scales and arpeggios? Comment below!