I don't see this happening. Even if they were to be placed on hiatus, they would likely be returned much like the fire flower was after a period of absence.
Let's use Super Mario 64 as a good save-based game example of why the 1-Up mushroom is still useful. Suppose you are in Lethal Lava Land and are trying to get the fifth star (one of two inside the volcano). When you re-enter the painting, you are placed directly into the volcano and no longer have to find a way inside. Yes, there are wing caps and shells available to get there, but some players (especially younger ones) may have trouble with coordination and need to try many times to reach the inside of the volcano. By accumulating 1-Ups, the player may have, say, five chances to reach the inside (instead of one). There are other moments, in both 64 and subsequent games, where the same thing happens (it's nothing new, either--even the original SMB had the midpoints in each level).
Also, some of the more recent Mario games (64, Sunshine, and Galaxy) have required the player to go to a particular area far away from the starting point, which often is a hassle for those who are very focused on the level at hand. I think we've all had to do this at some point or another. In this case, having extra lives is a blessing.
If there were no 1-ups, we'd be stuck with the following alternatives:
-Start the game over from the beginning (not really an issue with the way modern games use saves, but think about, say, playing on a GameCube without a memory card)
-Give the player infinite lives a la Super Princess Peach, taking away the challenge for more experienced players
-Make the player go to a far-away area every time they die (think about some of the places in Sunshine for an example)
The current system works fine as it gives a nice compromise between helping out and adding to the challenge--the challenge of the level and also to accumulate these mushrooms is still there, but there are still consequences if the player dies too much.