I support the idea of an amnesty in principle, but I don't think it would work in practice. After 911 loads of scummy scammers came forwards to fraudulently claim benevolence money for invented relatives. People falsely claimed to be at the Ariana Grande concert that was bombed to get tickets to the benefit gig. A small number of scumbags will take advantage of a tragedy, by seeing a loophole of opportunity for personal gain. An amnesty gets us no closer to the truth and may even set it back.
The situation at Grenfell Tower, before the fire, will have been messy. Layers of subletting and sub-subletting going back years, poorly managed tenants' lists, rent a room, sofa surfing, Mon - Thurs lets, airbnb, mini dorms of undocumented overseas workers. There's a black economy in the labour market, and it's just as reflected in the housing market. Part of the legacy of this tragedy is that the inferno took a snapshot of life in one community in modern Britain. Everyone who was there that fateful night got caught up in a tragedy that was decades in the making by various policies and political philosophies that have shaped the legislative and governance frameworks over the years. Sadly the identities of many of the deceased will never be able to be acknowledged or recorded. We have such a patchwork of housing situations at the sharp end of the market, and it means so many get pushed through the cracks.
If the amnesty were simply linked to the investigation, and not access to long term housing or indefinite leave to remain I could be behind it, but I don't see how you'd separate them out.
The legacy moving forwards must be to crack down on unregistered subletting. People breaching rules for personal gain runs from the bottom to the top has contributed to this tragedy. Subletting won't have caused it per se, but contributed to extra people causing panic on the stairwell as well as the impossible task of ascertaining identities.