Can my US employer just put me on their US payroll even though I live and work in Ontario?

No, not correctly, an employee who lives and physically performs all their work in Ontario generally needs to be paid through a properly set up Canadian payroll, with Canadian income tax, CPP, and EI source deductions withheld and remitted, rather than simply being kept on the employer's existing US payroll system because that's administratively easier for the company. Canadian source-deduction obligations attach to employment duties actually performed in Canada, regardless of where the employer happens to be headquartered or which payroll system it already uses for its US staff.

Employers who simply keep a Canadian-based remote hire on US payroll are often doing so out of convenience or oversight rather than because it's legally correct, and it can leave both the employer and employee exposed, the employer to Canadian withholding, remittance, and registration obligations it hasn't met, and the employee to confusion about which country's tax and payroll rules actually govern their pay.

Many US companies handle this properly by registering for a Canadian payroll account directly, or by using a third-party payroll service or employer-of-record that specializes in employing Canadian-based workers on behalf of a foreign company, rather than trying to stretch their US system to cover an employee who doesn't actually work in the US.