1. Scales, arpeggios and broken chords help you learn key signatures. If you practise scales, arpeggios and broken chords in the same keys as the music you are likely to sight read, you are more likely to automatically play the right sharps or flats when you recognise that a piece of music is in one of those keys.
A quick way of working out which major key something is in:
For sharp key signatures, look at the last sharp in the key signature and go up one semitone from that. This will give you the major key. For example, E major has four sharps - F sharp, C sharp, G sharp and D sharp in that order. D sharp is the last sharp. Go up one semitone from D sharp and you get E.
For flat key signatures, look at the second from last flat in the key signature and this will give you the name of the major key. For example E flat major has three flats - B flat, E flat and A flat in that order. (This method doesn't work for F major which just has B flat in the key signature). Learn more about how to work out key signatures.
2. Scales, arpeggios, and broken chords help you learn a fingering system which you can apply to pieces of music in the same key. When you practise your scales, arpeggios and broken chords enough times correctly, your fingers will automatically use the most appropriate positions when you're learning a piece of music. Less time spent worrying about which fingers to use means you're more able to focus on working out the notes and getting the music flowing.
3. Learning scales, arpeggios, and broken chords also helps you memorise patterns that are commonly found in music in some form. Music often contains many passages that are based on variations of scale, arpeggio and broken chord patterns. Learning these patterns enables you to spot them or similar patterns when you're sight reading a piece of music, which makes the process a lot quicker than trying to work out individual notes.
This process is helped additionally when you include further technical exercises such as diminished 7th arpeggios, dominant 7th arpeggios, arpeggios in different inversions, whole tone scales, chromatic scales, scales in thirds etc. All of these patterns are commonly used in music in some form. Of course you don't have to practise all of the technical exercises all the time, but some experience of playing them definitely helps.
Read more about sight reading.
Read about how learning scales, broken chords and arpeggios comes in useful for improvisation.
More about why it is useful to practise scales, arpeggios and broken chords.