All Napoleonic armies used squares. Not aware of any authors who suggested the British drill was different to the practice of others re squares.
The Austrian Masse, a column which became a solid 'square' was specifically mentioned as it was different. Same with the British 2 deep line. I feel if there was only the British using a kneeling front rank in a square, it would have been remarked upon and praised by the more partisan British authors. But its not.
The strength of the square was not presenting a flank or gap to the oncoming cavalry. A solid wall of men with baynots would deter most horses and riders from closing. Not sure standing or kneeling makes much difference to that. Although more difficult to run away if your kneeling I guess! Square stays firm, it sees off the horse, wavers or not well formed and its in trouble.
Plenty of examples of Cavalry riding down squares as well as them repelling attacks.