On related note, when I arrange for ukulele and voice, I keep two items in the forefront. First, the vocal range (as it is the melody in this case) and next the key. This allows me to choose any of 5 (major keys) most of the time (C, G, F, A, and D). That gives you most of the range options you would need to have. As a classically trained musician with a PhD in music, I understand the thought behind choice of key, which could be intentional or pragmatic (Bach, for example, composed in specific keys for which the organ at the church was in tune). There are great arguments for keeping things in original keys--particularly with classical music...until you start figuring in the changing nature of intonation and how A has changed over the years.
At any rate, I can also move a song to Bb, as Eb is easy enough to play on the ukulele. But I do try to avoid songs that require an E.
My only gripe about The Daily Ukulele is that most songs are too low. Our local ukulele jams attempt to have people transpose on the fly...but in reality, a lot of people just need to play the chords they see.
As for E, the only song that I regularly play that comes across it is "My Favorite Things," which switches from an Em chord to a E in the third verse. I often jump to 4447 when playing it, as the higher sounding chord is as much of an audio "surprise" as the major chord...it seems to work.
The E Chord also shows up in my Hal Leonard Hymns for Ukulele "A Mighty Fortress Is Our God," printed in the 1402 variety...and what is funny is that I just play it without thinking about it.
All that said, I don't stop practicing the E chord in its various formations--and I am one of those players currently working on learning all the positions of all of the standard chords on the ukulele (jazz chords...another story), as well as picking up ability in fingerstyle and chord melody (closely related but not the same).
I don't try to convert all E to Em or E7 (as suggested by some), and my musical training and practice involves some level of stubbornness that if a song requires a chord, that I am going to play it. That said, I do see many instances of major chords used in songbooks or charts where the Dominant 7th should be used, and I'm not afraid to play the (harmonically) right chord in that instance.
So...I have offered a couple of song where I see E, as well as discussed my own thoughts on use of key...covering all the bases of answering the original question and going slightly off-topic or beyond topic at the same time.