That’s true. In fact, the first component to any speedrun is skipping all these upgrades. A lot of time is saved this way.
Prince of Persia 2 makes it impossible to skip the life upgrades! You start with 3 hitpoints, can get a maximum of 12, and need at least 11 to beat the last level. If you got to the last level with fewer than that, there is an endless supply of life-extending potions, but it takes time to get them, probably more than you would save by skipping the upgrades throughout the levels.
It is also worth mentioning, that (unlike in PoP1) there are more life upgrades scattered in the levels of PoP2 than the maximum number of hitpoints you can get, so some of them are worth skipping; speedrun experts know which ones. 🙂