DOGE has a limited issuance in a limited time and unlimited issuance in an unlimited time, which is both an advantage and a disadvantage. Dogecoin has inflation, while Bitcoin is deflationary.
Currently, and for about the next hundred years, Dogecoin's operation is similar to that of most other crypto assets and will continue to be so. The 'capped' assets are far from fully mined - and will continue to increase their supply in the foreseeable future, just like Dogecoin.
Dogecoin's supply is not infinite, as its issuance per block, per day, and per year has absolute limits - just like other currencies. The only difference is that Dogecoin's issuance does not have an end date. Therefore, Dogecoin is only 'infinite' in 'infinite time'. In a limited time, its issuance is actually limited.
Issuing once a year is to pay miner fees and ensure network security. Other blockchains, like Bitcoin, will theoretically completely stop annual issuance by 2140, at which point they will need to find a way to secure their network (if it still exists), otherwise, the design of their consensus mechanism will need to change drastically. In short, setting a cap on Dogecoin would make the network insecure and vulnerable to attacks. #doge⚡