【jQuery】jQueryでselectMenuを導入したらiOS Safariで動いてくれない話

<select name="speed" id="speed" style="display: none;">
	<option>Slower</option>
	<option>Slow</option>
	<option selected="selected">Medium</option>
	<option>Fast</option>
	<option>Faster</option>
</select>

<!-- タップすると下のプルダウンを展開 -->
<span tabindex="0" id="speed-button" role="combobox" aria-expanded="false" aria-autocomplete="list" aria-owns="speed-menu" aria-haspopup="true" class="ui-selectmenu-button ui-button ui-widget ui-selectmenu-button-closed ui-corner-all" aria-activedescendant="ui-id-28" aria-labelledby="ui-id-27" aria-disabled="false">
<span class="ui-selectmenu-icon ui-icon ui-icon-triangle-1-s"></span>
<span class="ui-selectmenu-text">Fast</span>
</span>
<!-- UIついたプルダウン -->
<div class="ui-selectmenu-menu ui-front ui-selectmenu-open" style="top: 97.1167px; left: 22px;">
	<ul aria-hidden="false" aria-labelledby="speed-button" id="speed-menu" role="listbox" tabindex="0" class="ui-menu ui-corner-bottom ui-widget ui-widget-content" aria-activedescendant="ui-id-27" aria-disabled="false" style="width: 256px;">
		<li class="ui-menu-item"><div id="ui-id-24" tabindex="-1" role="option" class="ui-menu-item-wrapper">Slower</div></li>
		<li class="ui-menu-item"><div id="ui-id-25" tabindex="-1" role="option" class="ui-menu-item-wrapper">Slow</div></li>
		<li class="ui-menu-item"><div id="ui-id-26" tabindex="-1" role="option" class="ui-menu-item-wrapper">Medium</div></li>
		<li class="ui-menu-item"><div id="ui-id-27" tabindex="-1" role="option" class="ui-menu-item-wrapper ui-state-active">Fast</div></li>
		<li class="ui-menu-item"><div id="ui-id-28" tabindex="-1" role="option" class="ui-menu-item-wrapper">Faster</div></li>
	</ul>
</div>

$(document).on('click', '#speed-menu li', function () {
	event.preventDefault();
	var li_index = $('#speed-menu li').index(this);
	$('#speed').val(li_index);
	$('#speed-button .ui-selectmenu-text').html($('#speed option:selected').text());
});