The status quo allows for what are effectively two separate nations to keep face and avoid disaster -- for both. It is a unique and somewhat absurd state of affairs for sure.
Long answer is... Long. Probably reading on the history of China and what happened after the Communists won the war and the KMT retreated to Taiwan would be a good starting point to understand what's going on with Taiwan today.
( Edit : https://news.ycombinator.com/item?id=20263049 )
Also, no country in the world can have official diplomatic relations with Taiwan if they have them with China. ( Most do unofficially. ) Taiwan is consistently blocked by China from international organizations starting with the UN, etc. Not everything is as it should be in a 'truly' independent nation, with the status quo. A declaration of independence would therefore also affect every other country and the international order of things.
In fact, formally they still claim the whole of China since that's the constitution of the Republic of China, founded in 1912.
You'll note the portrait of Sun Yat-sen, first President in 1912 in the Taiwanese Parliament. And obviously the flag.
Based on this I believe that 'independence' means writing this off and declaring that Taiwan is not China but an independent "Republic of Taiwan" only.
This is exactly what I mean by political declaration and name change.