Feasibility comparison of symmetric ether synthesis and HCl + alcohol SN2 reactions

According to Solomons & Fryhle 10$^{th}$ edition Ch 11.8,



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> Because the chloride ion is a weaker nucleophile than bromide or iodide ions, hydrogen chloride doesn't react with primary/secondary alcohols unless ZnCl$\_2$ or a similar lewis acid is added to the mixture as well.
> 
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> 


However, we also know that symmetric ethers can be formed by an $S\_N2$ reaction between two alcohols, such as the synthesis of diethyl ether from two molecules of ethanol under [dilute acidic conditions](https://chemistry.stackexchange.com/questions/41574/controlling-the-reaction-of-alcohols-with-acid-to-either-ether-synthesis-or-elim), despite the fact that alcohols are generally bad nucleophiles.


With regards to the [Mayr-Patz equation](https://www.cup.lmu.de/oc/mayr/reaktionsdatenbank2/pages/show_page/7), ethanol has $N = 6.68, s\_N=0.85$ and chloride has $N = 13.00, s\_N = 0.6$ (both in 80% Ethanol, 20% water albeit chloride's $s\_N$ is estimated). Unfortunately, I don't know where to find the E value for a protonated ethanol.


Given this information, I'm now wondering if ethanol is necessarily always a worse nucleophile than chloride (considering it has a higher $s\_N$ value), and if it is worse, how is it possible for symmetric ether synthesis to be feasible with just acid, while $S\_N2$ happens at a negigible rate between ethanol and HCl?


