It's tempting to think that America's Covid-19 response would have been a lot better if Hillary had been president, but let's be realistic: the government's response would have been better, but the people would have fallen even harder for the "freedom" anti-mask/anti-vax movement.
There would have been mass protests from the start, with the GOP accusing the entire Clinton administration of being in league with a Chinese conspiracy to shut down the US economy. The GOP would have egged the protesters on with their usual brand of violent macho rhetoric and lurid conspiracy theories, supercharged by the resentment of having lost the 2016 election. By the time of the 2020 election, the loonies would have been bombing doctors' offices and shooting people for wearing masks.
The 2021 vaccine drive would have gone even worse than it did. With Trump unable to falsely take credit for the vaccine, he would have been openly against it, and Republican governors would have followed his lead in order to appease his fan base. Trump would have been almost as visible from 2016 to 2020 as he was in office, because the media loves him: he's ratings gold. He would have started his 2020 campaign weeks after losing the 2016 election, and he would have been holding his insane rallies this whole time.