Using https://github.com/joomla/joomla-cms/pull/5088 as a starting point, the JSessionHandlerJoomla method that does not read from JInputCookie works as expected on PHP 7 however the method using JInputCookie always fails to correctly start a session.

bad.php

public function start()
{
	$session_name = $this->getName();

	// Get the JInputCookie object
	$cookie = $this->input->cookie;

	if (is_null($cookie->get($session_name)))
	{
		$session_clean = $this->input->get($session_name, false, 'string');

		if ($session_clean)
		{
			$this->setId($session_clean);
			$cookie->set($session_name, '', time() - 3600);
		}
	}

	return parent::start();
}

good.php

public function start()
{
	$session_name = $this->getName();

	if (isset($_COOKIE[$session_name]) && is_null($_COOKIE[$session_name]))
	{
		$session_clean = $this->input->get($session_name, false, 'string');

		if ($session_clean)
		{
			$this->setId($session_clean);
			setcookie($session_name, '', time() - 3600);
		}
	}

	return parent::start();
}