How about to add options to the Menu Item -> Link Type: Link Attribute, Link Icon and Menu Subtitle?

Adding Link Attribute, Menu Subtitle and Link Icon (Image) from Media Manager

Or adding Link Icon like HTML

Result like this... In this case I used UIkit 3 framework.

<nav class="uk-navbar">
    <ul class="uk-navbar-nav">
        <li>
            <a class="joomla" data-attr="joomla" href="#" >
                <span uk-icon="icon: joomla"></span>
                Home
                <div class="uk-navbar-subtitle">Joomla! Start</div>
            </a>
        </li>
        <li>...</li>
    </ul>
</nav>

No matter what icon libraries or front-end framework you use.

Menu Subtitle option should be moved to some other tab... maybe...

Maybe someone would be able to implement this idea or someone sees this functionality as something else? ?