Whitepaper also says transactions should be cheap.
Anyone who chooses to pay more is a fool.
ETH Classic might be one example of a reorder / double spend but Litecoin and other smaller coins have not had that problem.
The whitepaper design, with halvings and all, may be flawed. But even if it isn't, it's obvious that the fees would be a greater source of income over time because there would be more transactions, not more expensive transactions.
The difficulty adjustment plays a bigger part in the security than fees. If fees drop, there will still be incentive to mine, likely from a more diverse pool of miners as operating expensive machines would not be cost efficient.