If only you were manipulating second only. You would also be manipulating metre, candela, and ampere, assuming old definition of SI, or metre, kilogram and kelvin assuming new definition of SI.

Can you explain how the duration of a second affects the metre?

Not OP, but "The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 second" - https://en.m.wikipedia.org/wiki/Metre

The duration of a second is defined using Caesium-133 [1], not using anything else like daytime or rotational speed. It's independent of such factors and will always be the same in a given frame of reference. No need to update those values.

edit: I think it will lead to the same or more problems because everyone would have to change all time-related constants. Easier to add a second to the day constant (because the day constant is a subset of the seconds constant, but the seconds constant affects many more aspects than just the day constant).

[1]: https://en.wikipedia.org/wiki/Isotopes_of_caesium#Caesium-13...

But in that case, doesn't the "second" constant change (or the coefficient) and a metre remains the same length?

A meterstick would remain the same length, but the SI meter's length would change.

Unless these physics constants are, well, constants put in the same code. How many ballistical systems treat ‘standard g’ as a variable? (hint: it depends on seconds squared.)