I have been to many, many business meeting meals, and individual receipts are required to submit for reimbursement, so restaurants that cater to professionals know upfront they will need to provide separate checks.
With friends and family everyone does separate checks unless one person is treating, and everybody is aware of that before we even get to the restaurant.
I do not think it is strange or rude at all to have separate checks--it makes it much easier and there are no bad feelings involved. Issues could include choosing expensive entrees, lots of alcohol, or even tip amounts!
With family, sometimes I will order a salad or dessert and pay for it, and then split the salad or dessert with another family member as I am not a big eater.
Of course, customs may be different depending on the part of the country, the relationship with the other dining partners, or even the culture(s) of the people involved.
The only time we would ever split the bill among the group and put all the money "in the pot" is if we would go to a fast food place or a diner.