The document's from the first 20 years of the 19th century suggest that delivery time for halves was several weeks shorter than for any other silver denomination. By requesting halves, depositors got their cash sooner rather than later. I'll pull up a couple of examples. Here's a quick one ----
April 27, 1829
The wish of depositors generally is to have their bullion coined with the least practicable delay, which is most effectually accomplished in the larger coins. An attention to their accommodation has been at all times deemed important, since the Government sends no gold or silver to the Mint. It was in this view, specially enjoined in a letter of the 13th June 1805, Mr. Mr. Jefferson to my predecessor for his guidance. The coinage of dollars was, however, suspended in 1806 by direction of the President under date of May 1 of that year, founded on a suggestion from the former U.S. Bank, that dollars were more liable to be exported than half dollars. This was referred to in the annual report of January 1, 1827 with an expression of an opinion in favor of this policy. Under the influence of these considerations, the determination [or] what coins shall be executed from time to time, devolves on the Director of the Mint, and is regulated with reference to the pressure of the supply of bullion, and the state of the machinery at any given time, the denominations less than half dollars being reserved for periods of a less copious supply.
[Sam Moore to N. Sanford, MC]