On top of drinking the spinal fluid, the shifter also needs to die at roughly the same time. Otherwise the power would just shift into a random eldian baby. This is why, when the beast titan gives his spinal fluid to a bunch of different towns people and government officials in the walls, they don’t turn into the beast titan when he activates them, they turn into regular titans, so it’s a bit of a process, but that’s ultimately why the titans eat people. It’s in their nature to eat and kill humans until they eventually eat a shifter. It’s not a conscious decision, but more of an instinct because they all ultimately come from the same being, and so they all have a shared knowledge that they act on without any will to control this. We see only two pure titans who fight this instinct off but neither of them are able to for long.