Help Text not appearing when using apex:outputField with a custom label

The solution is easy. Just use the helpText attribute of the apex:pageBlockSectionItem and put the help info from the field in it:

<apex:pageBlockSectionItem helpText="{!$ObjectType.Account.fields.Street__c.InlineHelpText}">
    <apex:outputLabel value="My Label"/>
    <apex:outputField value="{!a.Street__c}"/>
</apex:pageBlockSectionItem>

https://developer.salesforce.com/docs/atlas.en-us.pages.meta/pages/pages_compref_pageBlockSectionItem.htm

This is not a bug and works as designed and discussed in above document .

Note that if you include an <apex:outputField> or an <apex:inputField> component in an <apex:pageBlockSectionItem>, these components do not display with their label or custom help text as they do when they are children of an <apex:pageBlockSection>. Also note that <apex:pageBlockSectionItem> components can't be rerendered; rerender the child components instead.