Why is it that some people feel it's accurate to use a capo to transpose a song for easier playing, but then instead of putting the actual chords to the song, they instead write down the chord shapes they're using? (For example, a G major chord with the capo placed on the third fret is played as an E major). An E major chord is an E major chord no matter where you play it, and this goes for all chords.

I have a feeling that these people are too lazy to learn barre chords so they use the capo to find a position in which they can play the whole song with open chords (I'm talking about very simple songs, like Ed Sheeran's "I See Fire" and such). And that's all fine and dandy, use capos if you want to (and thank God you have a transpose function on the website), but that doesn't change the fact that a large percentage of these chords are incorrectly transcribed, and a beginner guitarist might find this very confusing.

So I guess what I'm saying is - use the capo if you want, just call the chords what they really are to eliminate all the confusion
Because writing the notes or chords that you're physically playing, without taking into consideration capo or downtuning, is common practice. For instance, all of the tab books I own, most of which are in either Eb tuning or C# tuning, have standard notation written as if they were in E. This is done because it, indeed, eliminates confusion. You don't have to completely revisualize you're entire understanding of how the fretboard works if there's a mutual understanding that you are communicating as if you were tuned to E. I've also seen countless instruction videos where a guitarist will immediately acknowledge that he is in a down tuning, or using a capo, and then right after will refer to his lowest open note as E. It really does makes things easier.
I don't agree, I think it makes things simply harder. Instead of putting down the names of the chords that are ACTUALLY being played, so that any guitarist or any musician anywhere can see it and immediately know how to play the song, you assume that everyone is going to be in E tuning and have a capo so they can play it like you play it. I don't use a capo, I don't like using it and I only have one guitar that is tuned down to Drop C/D standard. If someone does want to use a capo, they could simply transpose it down as many semitones as the number of frets he or she's skipping. I guess that's not a very popular opinion, though. xD
A lot of people who are interested in playing those types of songs are probably planning on singing them too, so it makes sense to keep the guitar fairly simple. Also, if that person is accompanying themselves with just one acoustic guitar, open chords are the best/easiest way to get a nice full and open sound.