When vacancies happen in the representation of any State in the Senate, the executive authority of each 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.
-- Seventeenth Amendment, Clause 2
A Findlaw article argues that an Arizona law that requires such an executive appointment be of the same party of the person being replaced (the governor of Arizona is now a Democrat) is likely unconstitutional since the provision gives the executive plenary appointment authority. In support, it is noted that those behind the amendment knew that legislative districts were malapportioned and in other ways might not be as reflective of the popular will as the governor. Overall, such a strict reading of the clause is plausible, but in no way compelling.
No evidence is supplied to show that those that framed/ratified the amendment was that concerned about malapportioned legislative districts. The essay ignores that current one person/one vote rules makes the issue much less a concern than it was in the 1910s. To the degree malapportionment still exists, as it surely does, would one person really be a better reflection of the complex nature of the electorate as a whole? The amendment was particularly concerned with senators being bought. Why would leaving it to the governor alone necessarily lead to less corruption of this form? And, yes, it's a good idea in a way to give the governor a chance to select the best person, "right" party or not. But, it also can be deemed more democratic to reflect the party of the person who the people actually elected in the first place.
The essay argues that it might be a good idea, for example if the senator left under cloud of partisan scandal, that the selection not be tied to his/her party. But, if we want to follow the exact text of the amendment in absence of anything else, it seems to give the legislature broad power when the people decide. IOW, "as the legislature may direct" specifically addresses that as compared to the executive appointment. In fact, this re-enforces my sentiment that a key reason for this option is that the legislature might not even be in session to "direct" anything at the time.
The essay argues that it promotes the "straightforward textual reading" of the amendment. Probably so, if not the only one, but such a reading of the First Amendment would also suggest "no" means "no" in all cases. Doesn't work that way. First, a reasonable interpretation can very well be that an ever existing executive might be the best able to fill the office because the legislature might not be in session for some time. Or, it might take too much time in general, an immediate appointment possibly the best policy (e.g., to cover the interests of the state or deal with a closely divided Senate). Some strings will not change that. Second, when a legislature "empowers" the executive to do something, it usually is inferred that there are some strings. For instance, can the executive set up a racially segregated panel to decide? Limits compelled by state law (and/or their constitutional provisions in particular) also might apply.
One clause should not be taken in a vacuum like that. This is not to say that it might be good policy to give the governor a free hand. But, I am not really convinced. If the governor refuses to follow the dictates of this provision (which will likely happen less than half the time), realistically, some compromise will be found. On the other hand, the governor might refuse to fill the office, leaving things to the people. Not a bad result really. Anyway, I do not think the amendment clearly compels plenary decision-making without any strings; a bare reading of text and history does not convince me otherwise.