There can be different motivations for this, ranging from mere bureaucratic "ostrich" cover-up, i.e. hope it goes away, which is probably what happened at city level in Wuhan in the early days, to more "rational" decisions not to do anything (or to implement limited/gradual responses), where "rational" means you have some other objective (to balance) than the short-term saving of lives. E.g. quote from a (former?) economic adviser of Trump:
“We put a lot of weight on saving lives,” said Casey Mulligan, a University of Chicago economist who spent a year as chief economist on Mr. Trump’s Council of Economic Advisers. “But it’s not the only consideration. That’s why we don’t shut down the economy every flu season. They’re ignoring the costs of what they’re doing. They also have very little clue how many lives they’re saving.” [...]
In novel outbreaks like this, a lot of the epidemiological factors that affect the severity of the outbreak, including the famous R0 (how many people get infected by one who already is) and the ratio of asymptomatic to symptomatic infections are initially estimated pretty far from their ultimate value, which affects estimates for the CFR (case fatality ratio) and IFR (infection fatality ratio).
For a past of such (over)estimation example see, H1N1/09.
"It's good to remember that when H1N1 influenza came out in 2009, estimates of case fatality were 10 per cent," said David Fisman, an epidemiologist at the University of Toronto, who was working in public health at the time. "That turned out to be incredibly wrong."
"As the denominator is growing in terms of case numbers, and case fatality goes down and down ... you start to realise it's everywhere," he said.
The prediction job is hard even for the experts; the WHO got flack [from some quarters] practically for every recent pandemic, for "calling it wrong", e.g. as reported at the end of January 2020:
WHO's cautious approach to the [Covid-19] outbreak, which has been challenged by some critics, can be seen in the context of past criticism over its slow or too hasty use of the term, first used for the deadly 2009 H1N1 swine flu pandemic.
During that outbreak, the UN health agency was criticised for sparking panic-buying of vaccines with its announcement that year that the outbreak had reached pandemic proportions, and then anger when it turned out the virus was not nearly as dangerous as first thought.
But in 2014, the WHO met harsh criticism for dragging its feet and downplaying the severity of the Ebola epidemic that ravaged three West Africa countries, claiming more than 11,300 lives by the time it ended in 2016.
There are various economic models that attempt to suss the optimal a response to an outbreak (see e.g. Stock, Eichenbaum et al., Ornelas), but they key message here is that these models are quite sensitive to the aforementioned biological/biosocial parameters of the outbreak. For a (great) visual clue as to sensitivity to parameters/assumptions, the Economist has this graph in an April 11 article:
... meaning that getting a slightly wrong estimate for a parameter can result in countermeasures way off the intended result-path, even when you have a clue what your objectives are...
Which for politicians can be even more complicated, if their main objective is to get re-elected (or not overthrown in a coup) because there's the additional proxying layer of how the public (or power players) are going to react/judge the measures relative to a counterfactual scenario that never plays out. Even when things "go wrong" in one country, it's fairly difficult even for experts to say why exactly (i.e. eliminate all confounders), never mind having the public make a correct cross-country assessment; see famous question here about the US public opinion on US vs. South Korea responses to the outbreak, which exhibited great polarization depending on the respondent's political affiliation.
So there are multiple layers on which a political response can "sink or swim". Additionally, there has been a rally around the flag effect for political leaders during this outbreak, apparently regardless of what they did, so to some extent they can "do no wrong" in the public eye in such circumstances i.e. when the outbreak does turn out serious/disastrous. (I'm guessing we'll see additional political science research on this in the future, i.e. whether the initial denialist/downplaying political response has any effect effect whatsoever on later public opinion or if it just gets completely swamped by the later swings in public opinion when an outbreak proves really serious, e.g. via "rally round the flag".)
Somewhat related: regarding how China eventually made the "right call" (when stopping the pandemic became their main objective), there's a March 31 paper (Tian et al.) in Science now on a model of their measures. This paper found that just shutting down transport from Wuhan or just implementing "Level 1" quarantines in cities with local outbreaks was not going to be enough in terms of limiting the pandemic. They had to do both. Which however is the most costly, economically, in the short run at least. They actually shut down transport from all affected cities, which in hindsight had no additional benefit though. And another point (of comparison) from that paper, with regard to H1N1/09:
The dispersal of COVID-19 from Wuhan was rapid (Fig. 3A). A total of 262 cities reported cases within 28 days. For comparison, the 2009 influenza H1N1 pandemic took 132 days to reach the same number of cities in China (see methods in Supplementary Materials).