Russia needs Crimea because without it they have very limited access to the Black Sea, and by extension the Mediterranean and the Atlantic; their other coasts, on the Baltic and in East Asia, are not adequate substitutes. The Baltic ports in particular tend to freeze in the winter -- not good if you have global superpower aspirations.
In the case of Taiwan, look at a map of China. Although China is comparable in land mass to the US, their sea access is limited to an eastern coast enclosed almost entirely by the South China Sea / East China Sea. Look at all the countries on the other side of the Chinese coast: Vietnam, Malaysia, Indonesia, Philippines, Japan, South Korea, and of course Taiwan. The US has military and naval bases in most of them. In the case of Philippines, Japan, and South Korea, the US has a LOT of naval bases, notably in Okinawa, halfway between Japan and Taiwan. This is no accident. In the event of conflict, the US could easily blockade China. A quick glance at the map shows how critical Taiwan is to this calculation. If the US controls Taiwan, it owns a huge island (a.k.a. unsinkable aircraft carrier) staring down the middle of the Chinese coast. If China owns Taiwan, the east coast of Taiwan has direct access to the rest of the Pacific.
US geography is so OP that we don't realize how bad other countries have it.
(By the way, the other countries mentioned are also geographically strategic assets. Kuwait has 10 times more coastline than Iraq. Without Kuwait, Iraq has only a few ports available to ship out their oil, and no other ocean access anywhere. Israel also controls a huge chunk of the Middle East's Mediterranean coastline.)