So you want to reform the week, the only time cycle that hasn't been altered in millennia to sync it with... what exactly?

Different groups of time have different goals. Scientific and technical applications only use the second. Years are useful both for agriculture and astronomy. Year subdivisions, weeks and months are useful for legal, social and personal purposes: weekends, holidays, celebrations, birthdays, embarrassing familiar reunions and all that.

They neither have to be in sync with anything, just being useful to track days in a year, nor they need to be mathematically pleasant, any programmers worth their salt will write you a perpetual calendar generator in five minutes.