In foreign languages with a polite form of "You" (such as French or German), there is an additional question: should a website use the polite of familiar form.
And it's widely accepted that a website should use the polite form.
In Japanese, besides there being a lot of different levels of politeness, using "you" is still considered too direct in general. In conversation, it is to be avoided in almost all cases. It's common to refer to people by name, or by omitting/implying the subject instead of saying 'you'.
There are really interesting problems that you come across when you build multi-lingual interfaces.
Is it really widely accepted? I'm still weirded out when people use the polite form. Let alone computers, that's just silly.
Why would a computer/website be polite to me? They have no concept of these things. Just using polite forms doesn't mean you're being polite, you have to mean it. A computer is as of yet incapable of having intentions.
Why would a computer use the familiar form? It seems to me that I would uncomfortable if a computer, or worse, a web interface actively maintained by team of strangers, started to address in language that suggested a certain level of intimacy.
It might just be my youngness and general disapproval of the polite form speaking here. I really think English has gone in the right direction by removing their polite form in favour of being polite without senseless grammatical contortions.
It's a minor point but actually English has only the polite form. Stiff upper lip, and all that. "Thou" is the singular, but it isn't used much any more.
The computer isn't being polite to you, the company whose website you are on, is. In the same way your computer isn't being casual and friendly with you - the person who wrote you the email is.
Whether it's an app or a website, it's all just a conduit - and I don't think it's farfetched to say that by and large companies use polite forms when referring to their (potential) customers.
And it's widely accepted that a website should use the polite form.