I have no expert knowledge about differences in roadholding characteristics between tyres from different manufacturers, but I do know from personal experience that it is not a good idea to have one worn tyre and one new one on the same axle.
The CT is required every two years, which is far too long. High mileage drivers will need to change tyres in less than that time to be safe and legal. You have only to go out at night to know that two years is too long. Too many cars are being driven with badly adjusted or missing lights and if the problem occurred just after a CT, they could be driving around like that for a very long time. If their tyres get the same attention as their lighting, they are putting themselves and every other road user at risk.
My earliest memory of a tyre failure is from the days before tubeless. In a busy city street we saw a pre-war banger with an inner tube herniating out of a split in the sidewall. Onlookers were waving and shouting, but the driver carried on oblivious. It was only when the swelling was the size of a football and finally burst with a sound like a pistol shot that her stopped to investigate. Those were the days!