Your claim is empirically false. The total number of excess deaths was 81K in 2017, 158K in 2018, 101K in 2019. (You need to click a few buttons to enable data from past years.) The reason is that the sinusoidal amplitude is fairly small and is explicitly calibrated not to capture the flu. Look for example at the 2019-2020 winter graph: the empirical data matches the model until covid kicks in. For some reason, people die more in winter irrespective of the flu, and the sinusoidal component attempts to capture this effect.
Stepping back from the details for a minute: this is a 15-year long joint effort of public health authorities in Europe, with the explicit goal "to design a routine public health mortality monitoring system aimed at detecting and measuring, on a real-time basis, excess number of deaths related to influenza and other possible public health threats across participating European Countries." In terms of data analysis, their model is very simple, comprising a constant, a linear trend term for population growth, and a sine-wave term for non-flu seasonality. Do you really think that they would be so incompetent as to use a model that explicitly removes the flu, which is the very effect that they are trying to capture? Give them some credit, they know what they are doing.
Stepping back from the details for a minute: this is a 15-year long joint effort of public health authorities in Europe, with the explicit goal "to design a routine public health mortality monitoring system aimed at detecting and measuring, on a real-time basis, excess number of deaths related to influenza and other possible public health threats across participating European Countries." In terms of data analysis, their model is very simple, comprising a constant, a linear trend term for population growth, and a sine-wave term for non-flu seasonality. Do you really think that they would be so incompetent as to use a model that explicitly removes the flu, which is the very effect that they are trying to capture? Give them some credit, they know what they are doing.