$re = '/(?:<span[^>]*?>)(?!<a)(.*?)(?:<\/span>)/';
$str = '<span style="font-family: inherit; font-weight: inherit; line-height: 1.3;"> <b>including their</b> </span>
<span style="font-family: inherit; font-weight: inherit; line-height: 1.3;">StackOverflow</span>
<span class="MainLink" style="font-weight: bold"><a href="https://website.com/" style="color: #2f82de; text-decoration: none">link name</a></span>
<a href="http://www.google.com"><span>testing</span></a>';
$subst = "\1";
$result = preg_replace($re, $subst, $str);
echo "The result of the substitution is ".$result;
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for PHP, please visit: http://php.net/manual/en/ref.pcre.php