A lot of it surely has to do with reciprocity and not losing face at this point. It is indeed the case that the US (as of August 18, when the CDC page was last updated before this post) was still banning travel from China, pursuant to the January 31 presidential order. But the Trump administration has repeatedly called it "the China virus" or thereabout (including at the RNC), so clearly they'd be losing face to some extent should they lift the restrictions on China (which in the meantime has imposed its own restrictions on the US.)
The EU's position vis-a-vis of China (mostly driven by France's insistence according to the BBC), but also reflected e.g. in the government of Netherlands statement has more explicitly to do with reciprocity at this point:
the ban on travellers from China will be lifted once China allows entry to EU citizens.
So clearly some of the restrictions have stopped being purely medical and have turned political. That's not to say they are entirely political. When the EU imposed/revised its new standards this summer, the number of infections in a region was a clear criterion:
The number of new infections must remain at or below approximately 19 per 100,000 inhabitants. Consideration will also be given to contact tracing efforts and the number of coronavirus tests carried out.
In the meantime the number of cases in the EU has increased substantially again, no doubt in large part due to the relaxation of internal infection-control measures... A number of the new restrictions imposed by some EU countries (on each other) were motivated by these developments, e.g.
On Sunday the Czech Republic recorded a daily record rise for the third day in a row, with 1,541 new infections. Neighbouring countries have begun to restrict entry for Czechs, with Germany announcing it would require a negative test for arrivals from Prague on Wednesday.
This is hardly the only example though of such recent changes. Over the summer the UK imposed quarantine on its own citizens returning from Spain, then from France and the Netherlands; at least the Netherlands was explicit in why they answered with similar measures:
A spokesman for the Dutch Ministry of Foreign Affairs said, "This means that Great Britain will receive a code orange as travel advice, because the Dutch have to be quarantined there."
Greece, Denmark, Belgium and Luxembourg (and probably more) imposed a test-taking measure on travelers from Bulgaria and Romania; Italy imposed a outright quarantine on them etc.
If you want to hear recent & explicit argumentation from a country that has almost totally closed its borders (back in April 3 billion people lived in such countries), Hungary has closed its borders to practically everyone, for the month of September, the reason given being that most infections are of "foreign origin":
"From September 1, foreign citizens will no longer be allowed to enter the territory of Hungary," Gergely Gulyás, the prime minister Viktor Orbán’s cabinet chief said during a press briefing.
"There is a risk of introducing the virus and most of the new infections are of foreign origin," he said, adding "Hungary is green, all other countries are now turning red," in reference to the traffic light system.
[...] Hungary's government indicated that the border closure will stay in place for a month.
So you could probably divide the reasons for the lingering and new restrictions in 3 categories:
- old restrictions not re-evaluated for various reasons
- new restriction imposed on countries perceived to be "high risk"
- retaliatory (tit for tat) measures