If I look at the last eight blocks (395,151-395,158) I see that 16,093 tx were processed for a fee of 3.08 BTC. That's 0.000191 BTC/tx or USD 0.0766 . I'm not sure how much zero-fee transactions are in there, but with an average of 7.7 cents, how much higher should the minimum fee bee in your opinion?
The average is problematic because there are some guys who are paying A LOT of fees without actually needing to pay them:
https://bitcoinfees.21.co/Anything above 50 satoshis/byte right now is overkill, yet some are paying >100 satoshi/byte which distort the average, while a lot of txs are in the 0, 1-10 and 11-20 satoshi/byte categories.
A lot? The past 24 hours only 1,079 free txs were processed, and 33,447 cheap ones (1-20 shatoshi/B). Compared with the almost 200k other txs, that's only 0.5% zero-fee and 14% cheap-fee txs.
That's 33.447 transactions too many.
Practically, except those who overshot the fees at the bottom of the chart, everything included are cheap txs. There is nothing expensive at sub-10cents (not that 10 cents are expensive). The 14% is just ultra-cheap / near zero cost and most of the rest are slightly above ultra cheap.
If you have an average of even 30 satoshi per byte, then 1megabyte will cost ~0.3btc, a gigabyte 300 btc and a terabyte 300k BTC.
That's just 120mn USD for fucking up the blockchain / bloating it 15x upwards, while the marketcap is valued at several billions

With half the fees (15 satoshi), it goes to 60mn usd for a 1TB attack. With larger blocks it becomes much easier and faster to accomplish if miners don't start cutting the trash off.
With "cheap storage" like this, even a third party enterprise can come aboard and say I'll use the Bitcoin blockchain for distributed storage of 50-100-200 GB for the X or Y application where I'll be using modified clients to pull out the data. And yeah, I'm willing to pay your peanuts in fees to do that, why not.
If we assume that people paying more than 20 s/B fee are not spammers or abusers, then we gain only 17% in capacity by further pushing zero/cheap tx out of the system. That's peanuts. It means that if the 1 MB tx supply quota stays intact, some Bitcoin usage simply has to stop in favour of better paying usage. Given how small Bitcoin still is, that's pretty sad.
10, 20, 40, 60 s/B, are all peanuts - not serious fees. 1c, 2c, 5c, 7c it's all way too cheap.
But if you can get away with abusing the network with the lowest possible cost, why not.