When a wiki is private (i.e. anon 'read' is disabled), then it would be expected that blocking a user will also remove their read access (i.e. it removes all of the extra rights that their user account has granted to them). However, that is only the case when $wgBlockDisablesLogin is set to true - and by default, it's set to false.
Of course, setting $wgBlockDisablesLogin to true by default would lead to unexpected behaviour in other situations (e.g. on Wikipedia, when logging into a blocked account you wouldn't be able to read any content, so you'd have *less* rights than an anon user has). So a simple 'yes/no' answer doesn't work here.
One possibility would be to make the default $wgBlockDisablesLogin setting conditional on whether anons can read the wiki - if they can, then it's false, if they can't, then true. That could then be overwritten by specifying a setting in LocalSettings.php.
Another one would be to add an option when blocking a user to also remove their read access (either by Special:Block and/or Special:UserRights).
(As a secondary issue: I note that while the default text at Special:Block does indicate that it blocks editing, it doesn't specify that it only blocks editing and not reading, and nor does that text change if $wgBlockDisablesLogin is set to true...)