The only rationale I could see for a rule is if they're running the tally themselves.
No, the rationale is obvious: it guarantees the total when the Big Bet rolls around is a nice round mathable-and-divisible-by-2 number, no more, no less. This also keeps Jim / Bob from having to do funky math (or relay a funky number if someone else is doing the math) when they are telling the player what the minimum Big Bet is.
It's simple, it keeps everything in nice round good-TV numbers for the folks at home, and the only people it affects negatively are the pedantic jackoffs who don't deserve the courtesy anyhow.
(And drawing a parallel between a light, fun gambling game like
Card Sharks and The Ultimate Hardass Quiz that is
Jeopardy! is one of the bigger apples-and-oranges comparisons I have ever seen.)