Thanks for reaching out.
Are you referring to the Admin > Appearance > Menus and the menu is too slow to load and edit? I think yes since you mentioned
Those custom fields are available in Appearance > Menus are Pro feature, it's primarily made for Pro header builder and you can't disable the cornerstone, and we don't recommend disabling it either. I have an underpowered machine and none of these issues are occurring, so I'm not sure why it's happening on your powerful server. This issue usually happen on Shared Hosting, are you on shared hosting? An example here https://www.sitepoint.com/community/t/mysql-too-many-connections-error-on-shared-host-dilemma/24501. It's not actually too many connections, but the hosting only allow few connections hence triggering this issue as it reached the limit faster,
Any server should able to handle traffic from queries because it's designed for that (except shared hosting), else, it's badly configured where the database is not optimized itself.
Please remember that cornerstone and our theme only runs on top of Wordpress as the platform, and it only uses the functions provided by Wordpress. Our theme and cornerstone have no direct connection with the database as all are processed by Wordpress. If it's poorly coded then the Wordpress itself is the culprit isn't it? Because it's all about Wordpress standard and it should be followed. I'm not saying there are no poorly coded plugins, there are many since they didn't follow Wordpress' standard.
Now, back to the performance subject, there can be two possible causes, the server-side issue, and the browser side issue. Both are triggered by a large number of menu items and it's true, but it's not a theme or cornerstone specific. Please try this, deactivate X or Pro theme, and cornerstone as well then try installing Ubermenu. Then add more menu items in Appearance > Menu while configuring it, you'll notice that as the items growing, it's getting slower at the same time. Try it on any plugin that alters and add features to Appearance > Menus, and it will be the same (like SuperFly). Those plugins have heavier feature than the custom fields like icon that came with Pro/Cornerstone and the builder is not even loading there, perhaps your hosting has just the very thin limit for allowed connections?
Again, I'm not seeing any connection issue on my machine but I could see it happen on menus with large amount of menu items regardless of the plugin (Ubermenu, SuperFly, and so on). You can try it too without the theme or any plugins, and it will be the same as long as you add too many menu items. This may help too https://wordpress.stackexchange.com/questions/115648/wordpress-menu-performance-is-slow-when-lot-of-items, https://www.wpbeginner.com/wp-tutorials/how-to-fix-the-custom-menu-items-limit-in-wordpress/