Dead people's identities are also great targets for e.g. spies, illegal immigrants, and money launderers, so governments have a strong interest in making sure the identities of the deceased get turned off promptly and thoroughly.
It’s amazing how lax the old paper system was.
Canada used to accept baptismal certificates as proof of birth in Canada. The Millennium bomber stole a blank form and got himself a Canadian passport pretty damn easily.
It’s not easy to get a death certificate (needs to be signed by a doctor or coroner) so reversing such an official document must be difficult.
And on top of that, there is probably no process for actually do it, so that’s a challenge itself.
Your attitude is - they know it will happen, it is rare so fuck it and lets ruin few lives so some government fucker does not have to strain all 2 brain cells they have left.
Btw when bad things happen to "important people" suddenly it gets fixed in no time.