Well if the network is dependend on fees only it means that the ones spending the coins will have to pay for the security of the ones not spending any coins.
I am pretty sure most coins will have to implement a constant block reward eventually(hard forkning). Here is some alternatives to...
Generally dash/darkcoin is very interesting currency but there is curently two issues i have with it
-already mined by asics when not even 50% of the coins has been minted
-exponential decrease in block reward, this is not needed for limited supply, it would also be limited with the block reward...