As stated above, it's a common misconception that bike tire caps prevent tires from deflating. Their main role is actually to keep the bike valves clean and intact. So, if you remove your bike tire caps, you won't have to worry about the tires immediately deflating or going flat.
However, without caps, the valves inside the tires can get damaged, and this may make them weaker and cause air to escape, leading to a loss of tire pressure and a higher risk of leaks. So, even though bike tire caps don’t directly control tire pressure, they do have an impact on it in the long-term, and using caps is part of good bike maintenance.