If it were me (it's not, of course), I'd require anyone who gets an account to affirmatively answer a question such as "I understand that by not providing an email address, it will be impossible for Wikipedia to help me access my account if I forget my password," and to do so before Wikipedia allows the account to be created.
In the larger context, when signing up for an account, a user should be able to specifiy, when providing an email address, that the email address can be used for [checking multiple is allowed]:
--- For recovering the account password
-- For welcoming emails from the Wikimedia Foundation
-- For other emails from the WMF
__ For emails sent by other Wikipedia users [making clear that this does not disclose the user's email to those other users]
The idea is to encourage users to provide an email address because they have more control over what it is used for.
A third leg of this might be to send a second, and maybe a third, email, if the first isn't responded to, explaining the consequences of not verifying the email address.