Better would be to require the election to fill a vacancy to be held within 60 days. Congress clearly has authority to pass such a law under the time, place, manner of elections.
Yes and no. The 17th Amendment didn't just copy the language on vacancies for the House and use it for the Senate. It added some extra verbiage.
When vacancies happen in the representation of any State in the Senate, the executive authority of such State shall issue writs of election to fill such vacancies: Provided, That the legislature of any State may empower the executive thereof to make temporary appointments until the people fill the vacancies by election as the legislature may direct.It also didn't strike the language that gave the States the sole responsibility for the Place of chusing Senators.
However, I agree that the Time power, which is what is under discussion here would fall under Congress's purview. However, that temporary appointment power is liked by the States and not just because of the political situations it can cause. It enables them to save the expense of a statewide special election by waiting until the next general election to hold it.