Issue with Bernoulli Pipe flow - Driving me mental

Ok, so I'm a third year ChemEng but ever since first year when this was taught to me I have never been able to understand it.

So imagine a horizontal pipe of which is a constant diameter. The pipe will have a given pressure at the beginning of the pipe and also a given flowrate. Given that the pipe has constant diameter this in turn must mean that the velocity is the same at all points within the pipe (continuity equation). Obviously, there will be pressure losses as the water flows through the pipe as a result of the shear from the walls. This is where my issue comes in. If the pressure is lost the further along the pipe you go, will this not cause the pressure to eventually reach 0? How is this possible? The water can't stop flowing as the volumetric flowrate must be equal at all points? It's baffled me since the day I learnt it.

Please don't think I'm stupid, promise I'm not. I've just never got this concept in Chem Eng for whatever the reason. Danke.

If the pressure dropped to zero there would be no flow in the pipe. To overcome this, either a more powerful pump would need to be selected, or different pipes (different surface roughness or diameter) would need to be used.

Why would the pressure being 0 further down in the pipe mean that there can't be a flow closer to the beginning?

It's been a while since I have looked at pipe flow, but I'm not sure if the equations suggest the pressure would eventually become zero (gauge or atmospheric).

But think about another example. You have a powerful pump connected to a short horizontal section of pipe, then an elbow turning the pipe vertical to an infinite height. Even though if you were to calculate the pressure at a point on the short horizontal section it should be high, we know that this then would not mean that the fluid would continue to be pumped to an infinite height.

This stuff is quite empirical and using the equations alone won't necessarily explain everything thoroughly.

I'm not sure what exactly would actually happen in the above example to the flow, although the basic equations probably won't tell us. Maybe a highly localised turbulent region immediately after the pump with much of the rest of the fluid remaining stagnant, I don't know...

Thanks, in all honesty I think the question I'm asking is one that doesn't really need answering, as in reality there wouldn't be such a large pressure drop that the pump wouldn't account for. Just one of the many things in Chem Eng that doesn't quite make sense to me!