While I understand your intent on saying this, I think the reaction you get is because that is essentially a Sycophant which historically for the past known duration of human history has thrown vulnerable people under the bus in order to make the powerful more powerful.
I think what you probably want to say is that as a manager you should balance the 3. If you have to sacrifice the wellbeing of your employees or yourself for the company, well maybe the company isn't worth it. Also your employees probably don't like knowing you are making sacrifices for them instead of setting boundaries for yourself in order to take care of yourself. Nobody likes a martyr.
Especially in the tech world were theoretically you can leave a job and find a new one that doesn't conflict with this balance.
The general view in 2024 at least in my circles is to establish boundaries, find balance. Not blindly make the company your "#1 priority" in every decision.