Unfortunately as an at-will employee you can be fired for any reason, including absences because of sickness. But there may be an issue with the company firing employees because of their medical condition or disability. The company has an obligation under state and federal medical leave laws to provide unpaid sick time to qualified employees if they request time off to deal with a serious medical condition. If they instead just automatically fire an employee who is eligible for CFRA/FMLA leave who requests time off that may be an issue.
While employers may have attendance policies designed to encourage employees to maintain good attendance, there are certain types of illnesses or medical conditions which may not be used against the employee. For example, if an employer fired an employee because they have cancer, or a qualified disability, it would be violating the California Fair Employment and Housing Act. Also, large employers, such as Home Depot, (which, by the way, you should not be identifying here), are subject to the FMLA and the CFRA, whereby qualified employees who are seriously injured or ill cannot be disciplined or fired for taking up to 12 weeks of for the serious illness or injury. So a blanket policy, such as you describe, could well violate state and federal law.
They say you get what you pay for, and this response is free, so take it for what it is worth. This is my opinion based on very limited information. My opinion should not be taken as legal advice. For true advice, we would require a confidential consultation where I would ask you questions and get your complete story. This is a public forum, so remember, nothing here is confidential. Nor am I your attorney. I do not know who you are and you have not hired me to provide any legal service. To do so would require us to meet and sign written retainer agreement. My responses are intended for general information only.
You should refer to your employee handbook for details on how this point system works and how it applies to your situation.