Why didn't the U.S.A. or the U.K. think of putting a tube on their submarine?

They did. It was patented in Britain in 1916.

Like so many bits of military technology, it's not "why didn't they think of that". It's "why didn't they invest the time and money into perfecting and deploying it?" In the case of the submarine snorkel because its far more complicated than it seems, it wasn't as effective as it seems, and because they didn't need it.

The greatest threat to a WWII submarine was aircraft, and the Allies had air superiority. And the Allies weren't conducing major submarine operations in the Atlantic, while the Germans were. In the Pacific, the Japanese anti-submarine tactics were incompetent.

The Threat Of Aircraft

An aircraft could patrol a very wide area faster than a ship. It could see farther. It could appear out of nowhere, and attack before the submarine could dive. The introduction of rockets on anti-submarine aircraft made them even deadlier. A WWII submarine had no real defense against aircraft except to dive. The Germans tried with dedicated anti-aircraft Flak boats, but Allied aircraft quickly countered by massing aircraft against any U-Boat that chose to fight on the surface.

Even if the submarine was not destroyed by the aircraft, forcing it to dive would limit its speed and range. For example, a Type VII U-Boat could go 8500 nautical miles on the surface at 10 knots, but underwater it poked along at 4 knots for 80 nmi. The aircraft could remain overhead for hours, forcing the submarine to remain underwater depleting its batteries, which meant more time vulnerable on the surface charging. While the submarine was pinned in place underwater, surface vessels with sonar and depth charges would be on the way to find and destroy it.

Once there were sufficiently long range Allied aircraft and escort carriers to cover the whole of the Atlantic, the Battle of the Atlantic turned rapidly against the Germans. Comparing the map of U-Boat losses for 1941, vs 1942, vs 1943 shows the increasing role of aircraft in sinking U-Boats.

The Schnorchel And Its Limits

The Germans needed a solution to the increasing threat of Allied aircraft. A cheap answer was the schnorchel. Fortunately for the Germans, the Dutch had been experimenting with snorkel boats. The Germans captured a few O-21 class submarines which gave them a head start. Now a U-Boat forced to dive could charge its batteries underwater. This meant less time on the surface charging batteries. And a better chance to escape an aircraft should they be detected.

But it wasn't perfect. They were limited to 6 knots, still very slow. The schnorchel and diesel exhaust was visible from the air and detectable on radar, and Allied radar was getting much, much better. The diesel engines were noisy making the U-Boat easy to detect on SONAR, as well as making the submarine blind from its own noise.

A snorkel is so much more than "a tube with a valve on it". The US retrofitted their WWII submarines after the war with snorkels derived from captured German Type XXI U-Boats as part of GUPPY. Here is a simplified illustration of what's involved.

Source: The National Museum Of American History

It needed careful engineering to ensure water did not enter and flood the engine and boat. It necessitated poking two large holes in the pressure hull, something that no submariner wants. It required even more pipes and equipment in already cramped spaces to get fresh air to the main engines and exhaust away.

When water did enter the snorkel it would slam shut sucking air from the submarine interior causing the pressure to rapidly drop until the diesels could be shut down, a very unpleasant experience for the crew.

The Pacific

The Allies did not conduct large scale submarine operations in the Atlantic, there was no significant Axis shipping nor surface fleets to attack. There were some Allied submarines in the Mediterranean, but increasing Allied air superiority by 1943 muted the threat of Axis patrol aircraft.

Where the Allies did conduct a submarine campaign is in the Pacific and to very great effect. The Allies destroyed 75% of Japan's merchant navy, over half of that was by US submarines.

Japanese anti-submarine warfare and convoy defense was, to put it mildly, incompetent. Japanese destroyers prioritized night fighting and fleet action over convoy protection. Their sonar and radar were deficient. They never used the convoy tactics which were so effective in the Atlantic. No dedicated destroyer escort was developed until late in the war when it was far too late.

The technical deficiencies that plagued the US submarine fleet early in the war lulled the Japanese into a false sense of security. Once these were resolved in 1943 it was too late for Japan to react.

Allied submarines had little to fear from Japanese ASW aircraft. There were few of them, and they were not terribly effective. Growing Allied air superiority drove them from the sky. Eventually a simple lack of fuel and trained pilots grounded them. There was no need for the complexity and expense of a snorkel on Allied submarines in the Pacific.