Who would have been President? A President Pro Tempore and Speaker hadn’t been elected yet when Garfield died and this was before the Cabinet was in the line of succession. Chaos!!
I’m not saying that he should have shot Arthur immediately; he should have waited until Oct. 10 (when the new PPT was elected) to do so. (Well, not Guiteau, an accomplice.)
Of course, had the PPT become president, it would be much more difficult to argue that having legislative officers in the line of succession is unconstitutional, which I believe it is, and James F’ing Madison believed so as well (and argued as much when the Federalist Congress legislated so that the PPT and Speaker followed the VP, and Cabinet officers were left off completely, so that Federalists, not Democratic-Republican Secretary of State Thomas Jefferson, followed Pres. Washington and VP Adams in the line of succession).