From the sources I gathered, including the Senate's own, the answer to this may be rather mundane - if each state only has a single senator then if they fall ill or are otherwise indisposed, that state will remain with no representative at all, and also make it difficult to achieve a quorum.

As to why only two, the original logic behind seemed to have been that the Senate, as the upper house, must be more discerning in its members than the House of Representatives, the popular, "hot-headed" branch. Because of this it would need to be small. Since only one senator is problematic for the reasons stated above, the next smallest number was chosen.

See: https://www.senate.gov/about/origins-foundations/senate-and-constitution.htm#:~:text=Delegates%20also%20agreed%20that%20one,Senate%20to%20achieve%20a%20quorum.

And: https://constitution.congress.gov/browse/essay/artI-S3-C1-1/ALDE_00013339/