When you need medicine, do you pray instead? WTF with that false equivalence between physical objects? Well, at least they exist. A humorist said the same about the Sun, that can at least be seen. Is it projection because you worship with physical representations of symbols? A failed attempt to parody knowledge about the world? In any case, "atheist" is a straw man here, meaning anybody who's not as fundamentalist, it also suggests that they must necessarily worship something, even if subatomic particles, denying that it's just about non-belief. I'm personally agnostic.
Personally I don't think that I'd ask people to avoid praying for me, but I may suggest other ways to help if it's more realistic. If they feel helpless but can offer time, I might prefer presence and conversation, just so I can share, which may have psychological benefits. At least it's not an imaginary being. It's also useful with overworked staff, if you're cold it's easy for a visitor to go get an extra cover, if you suffer, it's more than only having a button to press. You're less likely to be mistreated is there's a witness.
Something that does bother me is when "prayer" is not really that, but some sermoning and moralizing, sometimes even including attacks directed at living people. Even Bible verses warn against this hypocrisy and there's a suggestion of a model prayer that doesn't do that. Or people who claim that they should have the right to yell anything at anybody anywhere, as long as they call it prayer, including hate speech. Harassment is harmful and often criminal.
Then imagine a setting where another suffering or dying person is around, witnessing that someone comes to only bless you, as if you're worth more than other people. At least that's what happens with people in the cult I was raised in. Also, imagine if they also visit not only to pray, but to check if you should be denounced for excommunication if they see that you accepted a certain medical procedure, like receiving blood. Or seeing that you have some luck charm or buddha around, OMG, the heretic apostate. Who wants that kind of "support" visit?
Would I ever pray? Honestly, perhaps, but I have lost the reflex to appeal to the supernatural when under panic. Interestingly, I rarely am in such panic anymore, possibly for my ability to better address issues with psychology and medicine. Perhaps also because I don't fear death as much as I used to and no longer believe in after-death beings, including those of human mythology who might judge or torture you there.
It's apparently normal to fear death less as one gets older. On the other hand, I was also raised with superstitions and even feared "demons" when young. I understand that they're only imaginary beings vehiculated by human culture today, a conclusion with healthier outcomes. It's also incredible the knowledge one can get when studying culture, religion, history and science, when free from such obstacles to thought.