Maybe the reason, other than bad writing, is that Zavala banned the practice because guardians leave the city behind to figure it out. That's what Ana did.

[u]Need to do a little setup here:[/u] We know the Traveler was discovered on Mars by an astronaut team sometime in the early 21st century, somewhere around 2013, I think, based on the opening cinematic of D1. We know that the Exodus Black crashed on Nessus over 500 years ago, because Failsafe says in one mission that all her 'friends' (the crew and colonists) have been dead for over 500 years. So, the Collapse happened over 500 years ago. We know that the gondola leading up to the Iron Temple had not been activated in over 400 years, per Ghost's dialogue in the opening mission of RoI. So, we know it's been more than 400 years since the massacre of the Iron Lords by Rasputin. Thus, Saladin is over 400 years old. Current speculations by lore gurus set Destiny about 700 years in the future. This gives us about 300 years to have had a golden age under the Traveler. Human lifespan tripled during this time, and great advances were made in technology. Then the Collapse happened and our civilization was all but completely wiped out. We were reduced from a high-tech species to one barely above the iron age. Tribalism and Feudalism ruled. Record-keeping wasn't exactly a priority at that point, nor was history: survival was first and foremost on eveyone's mind. I say all this in order to set up the following point: some guardians might have been dead for a long time before their first revival. Centuries even. Archeologists and historians have trouble even today piecing together information about ancient cultures of whom there is little to no written record; we can reasonably assume that a lot of records were lost during the Collapse, and with that loss it makes knowing our past incredibly difficult. We know that Guardians rez for the first time with total amnesia. Cayde or Ghost (don't recall which) even tells you that memory loss is a side-effect of first revival. Given total memory loss, and centuries of entropy eroding whatever evidence might have existed of who you once were, it's basically a fool's errand to go looking for your past. Some people get lucky. Ana rezed with her photo ID badge, clearly telling her who she once was. Shinobu was a mortal in the post-Collapse era (presumably in the dark age) and befriended some guardians (the Coyotes). One of their ghosts told her she had the potential to be a Guardian. She later died in battle alongside those guardians and was subsequently revived, either by one of their ghosts or by a guardian-less ghost that was with them. Those Guardians knew who she was before, as did the other mortals they were all fighting to protect. So she had people who knew her first-hand to help her with her identity. She also had her diary. Lastly, Shin Malphur. Shin was a normal human boy in the post-collapse era, and was raised by Jaren Ward, a Guardian. At some point after reaching adulthood, Malphur (presumably) died and was revived by Ward's Ghost. While there is nothing to confirm this directly, it's assumed that the ghost informed Shin about who he was before his death/revival. Side note: yes Cayde has his journal but there is no explicit proof it actually belongs to him. He woke up with it, but it might have belonged to someone he was with when he died, or he might have been delivering it to someone... we dont know. To conclude, the reason Guardians are told not to go looking for their past is because it's a wild goose chase: they're almost certainly never going to find anything, because they wouldn't know where to look without some kind of clue (like Ana's badge). Further, it's more practical: every Guardian is needed to protect the City; Zavala cant have Guardians running off getting themselves killed (permanently) just to indulge in a little curiosity. As Altmith put in his post: let the dead stay dead. You are who you are Now, not who you once were.

My guess is to let the dead remain dead. Who you were, your family and loves for the majority of guardians are long gone when you are brought back. For the ones who are still around, the guardian once resurrected has no memories of the life they lost and the people they left behind. They died and have not been reborn, just replaced. The person who was died and a guardian fights in their place with their body. Rummaging around in the past can only open wounds for those who may have been close to the guardian and inspire guilt, remorse, and pain for the guardian looking into a past that is not rightly their’s. So far as we can tell, the light too does not care what you were. While many of those brought back were normal people, soldiers, technicians, fathers and mothers, there are conceivably the bodies of war criminals and serial killers from another life walking around as guardians now too. How would you justify that to yourself? How would you react to discover a member of your fireteam murdered your family before either of you were brought back by the light? I say let the dead stay dead. The person you were died, let them have their rest.

My honest guess... because that would require breaking the player immersion. When players create their guardians, they tend to create their own back stories to go with those guardians. Some people pretend they are their guardians, others pretend they are playing the role of some other individual who's back story they design. If Bungie created a back story for the player's character, that would eradicate a rather large portion of the player immersion, especially if that back story ended up being something the player didn't like. The whole "guardians aren't supposed to look into their pasts" thing is basically just a plot convenient way of avoiding this. More than my own guardian's back story, however, I was curious as to why the writer's decided to make it sound as if the player isn't allowed to look into their guardian's past... but then I realize, it's just a poor effort by the writer of making Ana seem more like the "rebellious" and "strong independent" type because she's a rule breaker. Being serious... I've seen better writing in children's games. I believe the reason our guardian's "can't" look into their pasts is because when they died, decayed, and then were revived, the ghosts were unable to rebuild their guardian's memories based off of their dna alone. Similar to the way Wolverine from the x-men can't regenerate his memories when he is shot in the head. His brain regenerates, but his memories do not. After the initial revival, I believe the ghosts record our memories and re-implant them whenever they revive their guardian. That is just a theory however, as it's also very likely that this is just another plot hole that the writer's at Bungie couldn't be bothered to fill. As to why we're not allowed... as I said, it's just a means of making Ana sound like the strong, rebellious type.

I suspect the Ghost revived flesh, the lingering remnants of who we were are gone. Granted, over time, personality quirks etc will reassert themselves as time passes. Why don't we lose memory etc upon death and revival by Ghost? I suspect it's because the revival is instant; there's no pattern loss or degradation in neural placement. Just speculation. I bet the Vanguard doesn't want Guardians digging because the past is over and dead...and who knows what we were before? Killers? Liars? How much of what we are now is because of circumstance? Because of Ghost's interactions? Lots to ask...maybe Ana will shed light on this.