A procedure that is presumably permitted by said constitution, right?
Yes, the Spanish constitution does explicitly support state of alarm, which is a way to suspend constitutional rights.
https://english.elpais.com/politics/2020-03-13/what-is-a-sta...
The interment of Japanese citizens during WW2 is one example.
The only way good things get done is if people continually fight and push for them. Laziness will doom you, no matter what pretty words are on a paper somewhere.
And in a pandemic, "good things get done" has a very different definition than it does at other times, something no static set of law is going to be able to anticipate. You have to be active and you have to be flexible.
Certainly, many rights need not be affected by a pandemic at all, and countries that have tried to use it as an excuse to crack down on those rights should be condemned. For example, the Indian government has threatened freedom of the press by trying to censor news coverage of the pandemic. [1]
On the other hand, as an opposite extreme, freedom of movement is something that in normal times is considered a right, but absolutely can and should be limited during a pandemic.
Other rights are somewhere in between. For example, in the U.S., the use of the Defense Production Act to compel ventilator production could be considered a violation of economic freedom (which has often been thought of as a right, though it's not a Constitutional right), and it wasn't strictly necessary. But in practice there wasn't too much controversy over it; most people seem to tolerate the idea of the government temporarily commandeering the economy in emergencies, especially for something as obviously beneficial as making ventilators. (Though there might have been more controversy if a Democratic president had done it, but that's getting into the political weeds…)
[1] https://cpj.org/2020/03/indian-supreme-court-denies-governme...
It really depends on your personal definition of "ditched their constitution".
For example, Spain "declared state of alarm" which suspends temporarily some constitutional rights.