"The Biden administration will rightly be unhappy that a policy decision like this was made in the final days of the Trump administration", said Bonnie Glaser, an Asia expert at Washington's Center for Strategic and International Studies think tank, as Reuters reported.
U.S. -Taiwan relations have warmed considerably during the Trump administration.
But the visits were suddenly scrapped a week before Democrat Joe Biden takes office and as President Donald Trump faces an all-but-certain second impeachment on a charge of inciting his supporters to storm Congress last week.
Taiwan has lobbied the incoming Biden administration to ensure it remains a priority, and Hsiao, the representative to Washington, spoke in November to Antony Blinken, Biden's nominee for secretary of state.
But it also allows both Europe and Taiwan to dodge hosting what could have been potentially awkward delegations by an outgoing administration.
But European diplomats and other people familiar with the matter said Luxembourg's foreign minister and top European Union officials had declined to meet with him during his planned European trip this week. The Luxembourg leg of the journey was abandoned yesterday after its outspoken foreign minister Jean Asselborn branded Mr Trump a "criminal" during a radio interview.
Meanwhile MEPs in Brussels are hatching plans to woo Mr Biden in a bid to reset the EU-US relationship, which they say was dealt a massive blow by President Trump's leadership.
Beijing considers the democratically-ruled island as part of its territory despite their break since the end of China's civil war in 1949, when Chaing Kai-shek's Nationalist forces were driven off the mainland by Mao Zedong's Communist forces and fled to Taiwan.
China to provide Covid-19 vaccines free of charge
They noted that, as of now, 29 confirmed cases of anaphylaxis are reported with the Pfizer/BioNTech and Moderna vaccines. Statistics so far would indicate that if you're allergic to anything, wait before getting the COVID vaccine.
Under President Trump, the United States has established much closer ties with Taipei - ramping up arms sales and sending senior officials to the territory, despite fierce warnings from China.
The stakes are high. Last week, Pompeo removed all internal restrictions that regulated how USA officials interfaced with their Taiwan counterparts, a move welcomed by Taipei.
During the Trump administration, Taiwan has received unprecedented attention from the U.S.in the form of official high-level visits, support for Taiwan's inclusion in World Health Organization functions, and increased arms sales to the island. "It's possible that State Department officials remain cautious towards Taiwan, at least until there's more clarity from the top".
Craft had been due to visit Taiwan from Wednesday to Friday, prompting China to warn that Washington was playing with fire.
Protecting Taiwan, one of Asia's most progressive democracies, from a Chinese invasion has become a rare bipartisan issue in Washington.
China had said it was firmly opposed to the visit.
"Some kind of speeches as a result of dividing a society can really create this kind of problematics", she told BBC News last week.