They are forced to make that claim.
One political party does it a lot more willingly – the Chinese Nationalist Party (KMT). That’s because, historically, the KMT and the Republic of China are synonymous. The other major party, the Democratic Progressive Party (DPP), uses the Republic of China phrase only grudgingly. The DPP – the major party everyone knows wants formal independence the most, but can’t say it – is now out of office. But the DPP is overwhelmingly ahead in polls for the presidential and legislative elections scheduled for January 16, 2016.
Here’s one indication of how superficial and forced is the Republic of China/KMT party line: After KMT party leader, and President, Lee Teng-hui, who served from 1988 to 2000, left office, he no longer felt a need to maintain the Republic of China facade. So he promptly joined the openly pro-Independence Taiwan Solidarity Union party. Hardly anyone votes for that party – for fear of what China would do if it won.
One way to think about this is to look at the differences and similarities between the situations of Israel and Taiwan. Both face international legitimacy issues resulting in few or no embassies in their capital. Both were invaded by neighboring armies in the late 1940’s. The Israelis won what we now call the Israeli War of Independence. Big difference: The Taiwanese lost in their uprising against Chinese invaders, a short sharp war now generally given the inglorious title 228 Incident.
During the decades that followed, the local Taiwanese gradually co-opted the invaders, partly through wide-spread intermarriage. Because there are big cultural similarities between Taiwan and China, and because of widespread intermarriage between mainlander and local families, Taiwan has no internal ethnic conflict anywhere near as fraught as that in Israel between Jew and Israeli Arabs. But both face serious threats from one or more bigger neighbors – threats they counter with modernized armies based on, to a greater or lesser extent, American weapons technology.
One Israel/Taiwan difference is that Taiwan doesn’t face anything like the West Bank or Gaza. But even there, a slight parallel exists with Taiwan’s control of Kinmen and Matsu Islands, traditionally real parts of China.
Would Taiwanese want to because one with China if China became democratic? Not likely. Here I would think about Canada and the United States. Both have a lot of cultural similarities. And America’s president is roughly twice as popular as Canada’s prime minister – in Canada. This creates no groundswell of Canadians wanting to merge with the US. The US permanently lost any chance for that when it invaded Canada in 1812-13, just as China did when it invaded Taiwan in 1947-49.