Modal interchange: Ionian
The V7 is probably the most popular single chord in all of music, and so it’s no surprise that Mixolydian songs use it too. But it’s important to understand what it adds to Mixolydian, specifically.
First, it adds a very strong dominant return-to-the-I-chord pull. Mixolydian already has dominant-ish chords (♭VII, v7) that give you a pull that’s maybe 50-75% as strong, so it’s not necessary to borrow a V7 chord to have a song that works. When it’s borrowed, it’s intentional, and it brings a specific brightness: the leading tone, the ♮7. The ♮7’s brightness carries something like conventionality — that is, it gives a Mixolydian song the basic harmonic vocabulary of every pop song, every church hymn, everything that’s trained our ears to hear V7-I as “resolving back to home”.
Second, depending on where the V7 chord is placed, it can make the song sound more bluesy. With a I7 chord, a IV chord, and a V7 chord, you’re very close to all the chords of a 12-bar blues, just a brighter version. V7 to IV motion especially sounds bluesy, because that’s what’s at the end of a 12-bar blues.
But remember from the Dorian modal interchange lesson that you can borrow a IV7 chord from Dorian. So if you start with Mixolydian, and stack a borrowed IV7 from Dorian and a borrowed V7 from Ionian, that’s the whole 12-bar blues.
Bonus tip: the Mixolydian ♭7 is a ♯9 over a V7 chord. Spelled fully, it’s a V7♯9, a Hendrix chord.