How to override the language with apex:outputText for date formatting?

Question

According to the docs the outputText component is locale sensitive and can even override the language by setting the lang attribute.

<apex:outputText value="{0, date, EEEE}" lang="da">
  <apex:param value="{!NOW()}" />
</apex:outputText>

The above snippet, however, will always print the English name for the current day of week, for instance the expected output with Danish language is tirsdag but outputText prints Tuesday instead.

This applies also without using the lang override and instead setting the language on the user.

How can I make outputText respect the lang attribute? Or at least follow the user language?

P.S. A similar problem occurs with number formatting where outputText is always choosing e.g. the US decimal style regardless of using the lang attribute or the user language configuration.