Its not bad on its own, but paying the running cost of the network with inflation means the people who hold a token pay for it (indirectly trough inflation loses) not the people who use the network.
Staking however does not make sense if the reward is paid trough inflation that cancels each other out assuming most of the supply is staked. So where does the money come from that actually pays to run the network and pays the profit that stakers make? It must come from fees.
Now you have a misalignment of interests. User want low fees and high security and stakers want high fees (an potentially low security to justify more staking and staking rewards for doing so). The free market meets somewhere in the middle, however a blockchain was supposed to remove the middlemen that sucks out value and provides little and overprices benefits (expensive security). Now you have just decentralized the middlemen but its still there and sucks outs value optimized for profit.
Meanwhile the actual user already have aligned interest (secure and cheap) and the simplest way to make sure the actual user run the system, is if you remove the incentives.
If there is no way to make profit from just running it, then the only reason to run it, is if you make profit form using it. An backwards if you make profit form using it then you are willing to pay to keep it running an secure. Thats sustainable and optimized for use.
A PoS system could only be achieved, if all tokens are hold by the people who use the system and holding are directly proportional to their usage. For obvious reason this would never happen.