The reason for the minimum balance is that storage on chain is extremely expensive: all the nodes need to have a copy of it! Compare with Amazon S3, where only a few storage-optimized servers are storing your data.
The minimum balance is a way to pay for that.
The minimum balance is strictly better for the user than fees because contrary to fees, it is not lost: you can recover it after selling your NFT.
See Asset Limit Account and Minimum Balance - #2 by fabrice for details