Yes, it would indeed be completely unreasonable. Let me tell you why.
Almost every unit is going to have Covid patients. If you are on a designated Covid unit, at least you will know the patients are positive and have the right PPE. If you are on other units, people may be positive and you not even know it.
If this is that big of a deal, it may be this isn't the right job for you. Your entire career will involve you running toward the danger while others run away. You are every bit as likely to get Covid out in the community, probably even moreso, than at the hospital.
You are twisting yourself up. No, you aren't going to escape communicable diseases if you go into healthcare.