Even in the US, this largely depends on the restaurant... or more specifically, on the software (if any) the restaurant uses for their point of sale (POS) system. I've had servers tell me they can't do it by seat but that they can do it in half... and very occasionally, I've had them say the opposite... and other times, they won't split it at all.
I've not ever been a server but the way the POS system is designed largely determines how easy it is to split a check at the end of the meal. Some systems are pretty low-tech and, while they can pretty easily split the check in half, splitting on a per-person basis can be time consuming and pedantic.
On the other hand, some restaurants have fancy systems where the server enters the order by seat rather than by table, which means that the check is, effectively, already split. They can select the seat and swipe a card or tell the system to print checks for each seat, or for different groups of seats.
Here's an example from a restaurant chain here in Austin, Kerbey Lane:
image from Yelp
As you can see, each seat is totaled separately. I think there's also a total at the bottom of the receipt if one person is picking up the entire tab.
Now, I think the important thing - and where this actually gets into Interpersonal Skills - is to respect your server's time, particularly if it's a really busy at the restaurant. Before the meal, ask them if they can split the check either by seat or in half. Generally, if they know they need to do this ahead of time, they can make it easier on themselves at the end of the meal. Remember that if you're paying by seat, if you get any communal food (appetizers or desserts), someone will likely have to pick up the entire cost for it, so note who that person will be as well. Some systems may allow an item to be split in half but probably not in six. Make it easier on them and have someone pick up the queso alone.
If they agree to split by seat, particularly if you're in a large group (6+) and you're all paying separately, consider padding the tip a little for them. It takes a lot more time to run six cards than one.
It's definitely not rude, though. You're asking someone to do their job. They may be slightly inconvenienced because it takes a bit of time but by giving them advanced notice (asking permission) and a little bump in their tip (showing appreciation), you're showing that you respect them and appreciate their time.