The only exception to the enforced ring signatures on the Monero-network is the minting of new coins. Whereas every normal moner transactions is mixed, the “coinbase transactions” aren’t mixed.
The coinbase transactions can’t have any mixins because they are applied on the transaction inputs. So the Monero emission is transparent and auditable. This ensures no “hidden minting” can happen. All outputs on the blockchain can be accounted for. No moneroj can be created out of thin air.
Coins based on zero-knowledge proofs, such as ZeroCash, are vulnerable to a “hidden minting” attack or bug. These (unlaunched) cryptocurrencies rely on a group of trusted signers to “guarantee” that they destroyed the key that could create an unlimited amount of coins on their network.
The cryptography backing these coins is also very new and could contain some unknown unknowns resulting in very nasty attack vectors for either privacy or “hidden minting”.
Monero has an intial “bootstrap” emission of 18.4 million coins. After that a fixed emission of 0.3 XMR per minute will kick in, leading to a desinflationary situation. The inflation percent will go down each year.
Side note: Why is a permanent block reward implemented?
An issue with most cryptocurrencies is the development of a fee market. The narrative is that when you limit the block size, a fee market will eventually develop. But this claim is highly debatable. When the transaction fees are supposed to be the main incentive for miners to secure the blockchain, it is possible the current consensus model will not be sustainable.
At the moment, miners still act as they are expected: they mine on the longest chain. When they don’t do that, they risk loosing the block reward. But when that block reward becomes small compared to the mining fees, it’s possible miners will have an incentive to not mine on the longest chain and start a fork trying to “steal” high transaction fees which were included in the latest blocks.
Certainly big miners or mining pools have an incentive to do this, as they have a bigger chance to mine a few blocks in a row. This can eventually lead to one big mining cartel mining all the blocks, which is certainly NOT desirable.
Therefore, monero implements this “permanent block reward”. The block reward will never drop below 0.3 XMR, making monero a disinflationary currency: the inflation will be roughly 1% in 2022 and go down forever, but the nominal inflation will stay at 0.3 XMR per minute. This means that there will always be an incentive for miners to mine monero and thus keeping the blockchain secure, with or without a fee market.