It looks like your little demo program would be easy for you to modify to show us all that your assertions are correct.
Show us how your timer based clock keeps better time than the simpler implementation using only millis().
You should be able to have both methods in one program at once, otherwise one or both ways woukd be useless in a real program.
Perhaps you are right, perhaps you are setting up a straw man by using millis() in correctly.
a7