Is it necessary to use Apex Tags while constructing a Salesforce Visualforce page?

No,  it's not necessary you can use HTML tags instead of apex tag while constructing but it is compulsory to use HTML tags inside <apex:page>tag.

For example:

<apex:page showHeader="false" standardStylesheets="false" sidebar="false">
<apex:form>
<h1>Show/Hide HTML form Visualforce Example</h1>

<head>
<title>Test</title>
</head>
<div>
This content will not be toggled.
</div>
<apex:commandbutton value="Save Content" action="{!Save}"></apex:commandbutton>
</apex:form>
</apex:page>

Thanks.