There can be scenarios, I think, where we (society) do not want to deter someone from reporting an emergency due to fear of being identified. Off the top of my head, consider a situation involving organized crime taking place, where call centre staff (or law enforcement) may be compelled to leak the identity of a witness.
You're mentioning things like organized crime reporting, which are not emergencies. In that case, I'd expect someone to talk to someone in the police department in person, or through an intermediary lawyer - not 911.
edit: added the implied consent thought
I may have been unclear but I said crime "taking place", implying crime in progress. I think any serious crime in progress (theft, assault, murder, etc.) deserves urgent attention, regardless of it being undertaken by mafia or gangs or amateurs or professionals.
For other types of reports where you have the luxury of calling from an alternative location, you might call the local police or other services rather than the national emergency number (or at least that is how the emergency services are designed to operate in the UK)
However if anonymity is your primary concern then you're much better off using a burner or pay phone rather than your primary handset - regardless of the number you choose to dial.
If you want to report organized crime that involves the upper echelons of power, don't use cellphones at all.
I think that depends on which country you're in. In some places it's possible to buy a phone and SIM card with cash while wearing a baseball cap and hoody, and if you're prepared to pay huge pre-pay roaming charges you could use that phone in countries where it's not so easy to obtain a phone anonymously. Authorities will get a log of approximately where the phone was whenever it was switched on, so you'd only switch it on while calling from a crowded place. It's not perfect, but is it worse than restricting yourself to public telephones?
911 will always get your phone number, to make call-backs possible.
What global db do you envision that has everyone's accurate voice print?