I don't think I understood this point.
The suppliers are the stakers, and the cost is incurred by anyone running a full node.
Yes
But anyone running a full node can stake if they choose to, and would be helping the network if they did.
No. You have to also have coins to stake. Even if you have a few coins you are not a significant staker and have no significant say in the decision whether to include transactions (the next block will just include them even if you don't, and you will still incur the storage cost).
Unless you want the system to concentrate into one where only the largest stake holders actually run nodes and stake. (Not so different from the present, but is this really the ideal?)
Even then, there is a time disparity. Storage costs are paid to the staker now, but costs are incurred by anyone running a node in the future (or alternately in the past if you view the fee as backward-looking which seems to be implied by the structure). Again, trying to bring these into equilibrium has consequences that are probably not what is desired (set of node operators and stakers becomes static).
Interesting point - though this has a positive impact on the utxo assuming an implementation of pruning.
The concept was conceived "backward" as you suggest; with the anticipation that once an output was "under-water" it would be pruned and attributed as fee.