Mining is not just for distribution of tokens. I would argue the more important use is for maintaining the proof-of-work blockchain. There have been some experimental attempts at maintaining a distributed ledger using a proof-of-stake/proof-of-work hybrid, but I don't know of any successful attempts to do it without a proof-of-work component.
If you have an idea of how it could be done, you may have a shot at dethroning Bitcoin.
Ripple achieves ledger consensus without proof-of-work. Absence of proof-of-work is how it gets a new ledger (analogous to the block) every few seconds. The XRP fee destruction deflationary scheme is effectively similar to a proof-of-stake inflationary scheme, because as the total supply of XRP decreases, it benefits all XRP holders in proportion to their holdings.
If you have an idea of how it could be done, you may have a shot at dethroning Bitcoin.