Phish is my all time favorite band, so to answer the original question, "Are all of Phish's covers that good?" I think so. I've personally seen them play songs from The Who's Quadrophenia, Also Sprach Zarathustra (2001 theme), Peaches en Regallia (Zappa!), A barbershop quartet version of Amazing Grace, Boogie on Reggae Woman, Jesus Just Left Chicago (ZZ Top) and Frankenstein (Edgar Winter) just to name a few.
If you get the chance search for and listen to some of the covers they do. SouthPaw41L hit the nail on the head as far as the reason for their popularity, they are all virtuosos on their instruments. They were extremely tight when they were on, which was often. Sure, they had their "not so good nights", but the reason they sounded so good is that they could jam out any song, bring it in to outer space and then bring it back to earth again. They listened to each other play and reacted accordingly. The thing that they did very well was create tension, then resolve it. Trey plays blistering leads and interesting melodies, Mike keeps the funky bass popping, Page keeps everyone in check and Fishman is.......just Fishman, he has incredible timing and can play a mean vacuum.
Their original songs are of course my favorite. The beauty of Phish is that they could play ten songs in ten different styles. Bluegrass, Funk, Rock, Reggae, Classical, Jazz, Zydeco, Calypso, Disco, A cappella, Punk, R&B, Blues, Fusion, Ambient Trance.........name it and I bet they've tried it. They challenged themselves and also challenged the listener.
"A Picture of Nectar" is one of my favorite studio albums, but the TRUE experience of Phish is in the LIVE SHOW!!
"Set the gearshift for the high gear of your soul.........."
Peace in. Peace out.