Let us assign a minimum fee (FEE) for the ratio of number of outputs to inputs, a transaction with ratio n should offer n*FEE fee to be relayed or mined.
Transactions collecting dust would become cheap compared to those fragmenting.
Zero fee transactions should not be relayed or mined (other than of their ratio is below 1/FEE so they become free for collection of dust)
You can't just do that. Block size is finite. Ultimately miners will prefer transactions with more fee per kbyte of transaction data. Software could implement default rules which are against the miners best economic interests, but then many miners would just change it— and the inconsistency would be even worse.
For free transactions, or as a tie breakers for transactions with very similar fee/kb transactions which reduce the txout set are in the miner's (and overall communities best interest), but I don't think those cases are common enough to be worth solving alone. (E.g. addressing it only for free transactions doesn't even solve SD's 1e-8 BTC messaging). (though I do also think we should also strongly bias the free transaction logic to favor transactions which reduce the txout set size)
This is why I was suggesting a heuristic to determine the smallest output which is economically nonredeemable (because its value is less than the marginal fee that would be required to get the transaction mined in reasonable time). The idea here is to avoid creating outputs which will not ever be redeemed by anyone because they would lose funds by doing so (perhaps someday they'd be worth redeeming— except they'll have likely lost the keys long before then). This isn't quite the same as penalizing txout set bloating, but it should prevent there from being a disincentive to _de_bloat it.
I'm a little irritated that I wrote you a nice explanation about why privacy preserving behavior does not need to increase fragmentation, and relative to current behavior privacy improvements could reduce fragmentation... and you've ignored it and gone on saying that privacy is a major risk factor here, but oh well.