You're describing (almost) the play for a spot where the ball is downed in bounds inside the hash marks and it's a hurry up situation. There is a lot more that needs to happen on an out of bounds play. First, the side or line judge needs to mark the spot and put the ball down on the sideline so the Umpire can see where it's spotted. Then the Umpire needs to mark with his foot the spot according to where it's been marked on the sideline while the new ball comes on to the field. (The ball on the sideline is not put into the play -- it's just there to mark the spot.) The U puts the ball on the spot, and then the ref needs to look at it to determine down and distance or whether the line to gain has been attained and signal the box man and stick men accordingly. Only when the linesman to confirm that the stick and box men have the spot accurately will the U signal ready to play and will the ref wind the game clock.
It easily takes 10 to 15 seconds. Particularly if the play before gained yardage or will result in moving the sticks. The ref starts the play 15 to 20 yards behind the line of scrimmage. If there is a run or reception up field out of bounds, the ref and U both need to haul to get the spot. You also always have human error, such as the ball guy on the sideline getting the ball to the linesman (or side judge) to get to the U.
Remember, there can never be two balls on the field at the same time. The ball that is put back into play is NOT the ball that went out of bounds. In fact, the ball that goes out of bounds is not even the ball that is used to mark the sideline spot. So there are three balls involved and if the ball guy fumbles a little, or the U, or the linesman, it causes a delay.
When a team is clearly in two minute mode and conserving time, so that they are clocking the ball, the officials have an abbreviated process for getting the ball into play. And, perhaps not shockingly, the spots are not accurate. The stick and box men are by necessity given more discretion to judge the spots and set the pendant. But even in that mode, on out of bounds plays, there's rarely an issue since the clock stops when most teams would be in hurry up -- under 2:00 in the 1st half or under 5:00 in the second.
Bottom line -- you're confusing the procedure for putting the ball in play after an OOB with the situation where they will continue to use one ball during a hurry up on tackles near the hashmarks.