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The points in favor of the jump ball are that it's a fun and interesting individual and team skill for the players, and got the ball into play in a way that was no more prone to rough play than other aspects of the game are.
The point against was that it was hard to administer fairly. It's enough that the players need ball skills, should the officials have to have them too?
(A point that could be taken either against or in favor was that some players were much better at it than others, and that it was lopsided when a tie ball occurred between players of much different heights. These are the sorts of considerations that are as arguable as any other design feature of the game.)
Australian football in recent years has shown dissatisfaction with similar procedures. They used to have an official bounce the (oblong) ball hard straight down against the ground, and lately have gone to something looking more like a jump ball. They used to have an official throw the ball in backwards over his head into the field to resume play from out of bounds; I forgot what they're doing instead of that now.
Speedball uses a kickoff to start periods, but as far as I know still uses a jump ball to resolve tie balls. As far as I know, team handball has no similar procedure.
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