It's not not true. We eradicated SARS by similar methods. It's just that covid is more difficult.
SARS (the short form always refers to SARS-COVID-1) was a more peculiar virus than covid-19. It wasn't nearly as infectious and you couldn't transmit it during the incubation period, only while having symptoms. The outbreak lasted for nine months, but fewer than 10,000 cases were reported. It spread to many countries from travellers who had been in Asia, but with other community transmission ever being established. This is possibly because it was a MUCH MUCH nastier illness than covid-19. In the older age groups, more than half of cases died. The overall mortality rate was 50 times higher than with covid-19. Either way, the measures taken were very different. There isn't much point of comparison.
Covid-19 behaves a lot more like the four endemic coronaviruses that are sometimes said to cause the common cold. In fact most colds aren't caused by coronaviruses and the coronavirus colds are probably at the bad cold/ maybe it's flu end of the cold spectrum for most people. Probably it will end up being the fifth of these, and endemic in the human population. In the future, elderly people will already have been exposed to it many times while younger so it won't be as deadly in those older age brackets.
If the exact same virus had started spreading before PCR testing technology or genetic sequencing, we would have done nothing to begin with. By late March there would have been clinical evidence of a nasty respiratory virus circulating.
Because people weren't panicking, elderly patients wouldn't all have been chucked out of hospital taking the virus with them, and so the transmission in care homes would have been much lower. This alone would have saved many lives. And because the virus would have been taken as flu/a nasty bronchitis, the treatments that actually turn out to be somewhat effective (oxygen, steroids) would have been tried earlier. People wouldn't have died unnecessarily because they were put on ventilators.
In the meantime, the virus would have continued circulating at very high levels in the non-vulnerable population and by the early summer most of us would have had it and developed some kind of immune response. This would have protected the vulnerable people who hadn't yet been infected, and the virus would have started being transmitted more and more slowly. Eventually, it would have behaved more or less like the other four coronaviruses which are found all across the globe and which in elderly people can cause serious illness. But none of us (other than virologists and medical professionals) would have heard of it. As it is, a lot of people seem completely to have lost faith in the capacity of human beings, either individually or as a species, to survive infection. In fact, our immune systems are, 99% of the time, awesome things!