On MOBILE platforms, Safari has a 25% market share in the world, a significance which its desktop counterpart cannot claim. However, in the US alone, where the share of Apple devices is higher than anywhere in the world, Safari's share is upwards of 50% in the mobile market. It would be worrisome if UA still doesn't support the most-used mobile browser in the US.

I can't remember having significant negative experiences with Safari. You could be using parts of Safari without knowing, as many iOS apps use the Safari framework to load and render specific content. There's no reason why UA couldn't make the seat map work on Safari.