I don't think your assumption is necessarily correct... Sure there are a lot of people who compile these apps up to native, but I also suspect a lot of Sencha's customers (especially the ones paying top $) are deploying it as a webapp, saved to iOS homescreens or whatever, for accessing intranet-style data.
I'd personally say the MVC nature of the framework lends itself better to app-like behaviour, whether it's deployed through a browser or native app, rather than just website data. But you could still very much use it for that - just by setting the html config on your containers within the pap.
I personally doubt, if ST is suitable for creating public mobile friendly websites, because not all devices are supported. Especially a bit older and hardware-weak devices have problems running ST-pages satisfactory.
So I consider if it is better to use some more lightweight framework for creating a mobile-friendly website?
Again I'd say it varies from case to case. If the visitors to the website still use non-webkit devices or Android 3, you need to take a look at what percentage of users that would be and make a sensible decision from there. Another reason why larger companies might trend to Sencha more - because they have control over the devices they are issuing to employees!
Also, if you want a mobile version that is more closely related to your desktop website, other options will allow you to do this easier by printing out HTML from mobile specific templates. Whereas Sencha Touch auto-generates all the HTML itself.
From a personal perspective, I've tried most of the other significant offerings out there. I'd never venture from Sencha Touch unless I had to, even if the support and communication from Sencha is dodgy at best... people always have the fallback of your main website if their device isn't supported by Sencha Touch, and the framework really is a joy to work with, as cheesy as that sounds!
In our case, it is not so important that the mobile version resembles the desktop website.
I would love to use ST, because I am starting to get experience in using the framework, and appreciate it more and more. But there is a voice in the back of my head, that says it would be wiser to use e.g. Bootstrap for the task. I wish that voice would go away :-)