(Yes, I know, "schedule the Senate's business efficiently" sounds silly, but it would be worse if everyone got ready to process a bill and only then found out they couldn't get to it).
Greg Koger covered this in his current book on the filibuster. I'll quote some of the highlights:
It is unclear when the hold system began. Senator Byrd (D-WV) coordinated the system as majority whip in the early 1970s, and this is often considered the origin date....However, there is strong evidence that senators placed holds long before the 1970s. The earliest known reference to a hold is in the DPC [Democratic Policy Committee] Minutes for August 5, 1958. Lyndon Johnson refers to a letter he received from Senator Chavez (D-NM) requesting that HR 7168, a bill setting policy for construction contracts, be held until he had completed some hearings. The DPC granted this request and held the bill...
Furthermore, a DPC offshoot called the Legislative Review Committee (LRC), also known as the Calendar Review Committee, also received objections to legislation...[T]he LRC would...act as a proxy for other party members by vetoing bills on request...The LRC would bock these bills in a manner that obscured the identity of the objecter.
The DPC noted the effects of accomodating senators' requests to schedule legislation around their absenteeism: "Senator Russell said he objected strongly to the practice of holding up bills because a Senator would be out of town and he considered it a new development which flowed from the elimination of the old system of pairs" (DPC Minutes, March 6, 1959). Russell repeated this claim weeks later. (References and footnotes removed; emphasis added).Richard Russell, by the way, served in the Senate from 1933 to 1971, so if he thought that holds were new in 1959, he probably knew what he was talking about.
So: holds were not a leftover from the 19th century; to the contrary, they were invented in the postwar period because of the demise of older traditions. Moreover, while their original use had to do with a temporary pause while a Senator was away or had some other reason for a short delay, by the time the current hold system was set up in the 1970s, it was transformed from a "wait a minute" kind of thing to the current filibuster threat. But the key thing to keep in mind is that holds were, originally, respected by the majority because it helped them run the Senate more easily. I believe that's still the case in general, but I also think that the majority has to keep in mind that holds are there for a a variety of reasons, and when those reasons don't apply -- as I contend is the case when small minorities seek to permanently block judicial nominees -- then there's no good reason for the majority to respect those holds.