InputField datePicker is missing when standardStylesheets are disabled in Visualforce Page

Sample Code:

<apex:page standardController="Opportunity" showHeader="false" standardStylesheets="false" docType="html-5.0">
   <apex:form id="frm">
      <apex:pageBlock title="Opportunity">
         <apex:pageBlockSection title="Opportunity Information" collapsible="false">
            <apex:inputField value="{!Opportunity.ClosedDate}" showDatePicker="false" type="datetime-local" />
         </apex:pageBlockSection>
         <apex:pageBlockButtons>
            <apex:commandButton value="Save" action="{!save}"/>
         </apex:pageBlockButtons>
      </apex:pageBlock>
   </apex:form>
</apex:page>