Beer's Law gives you the concentration that is in your flow cell when you take the measurement. Unless the entire peak is in the flow cell at one time, that doesn't directly tell you how much analyte came out of the column (that's why you integrate to get the area under the peak.
Different compounds have different UV spectra, so the calibration plot will be unique for a given compound. Different instrument/column combinations have different amounts of band broadening, so the calibration plot will be unique to a given system. And slight differences in mobile phase composition can make peak areas (and UV spectra) shift, so the calibration plot will be unique to a given day.
Bottom line: you have to calibrate the response factor for each compound on each system each day.