Running out of water is no big deal if it's the end of the day and there is only a short walk between you and the car. It is a big deal if you're partway through a route that's taking longer than you expected, or if you hope to recover quickly and send again tomorrow.
While creeks and lakes aren't usually readily available on alpine routes, snow is often not far away in most major mountain ranges. Even here in the sunny Sierra snow lingers in nooks and crannies throughout the summer. I've topped up my water supply from a melting snow patch on top of Mount Darwin even as late as the end of August.
If you've got a stove and fuel turning that snow into water is easy. It was above freezing on top of Mount Darwin that day in August, so I just set my bottle upright on the ground under the edge of the snow patch where it could catch the drip. Sometimes it's a bit trickier than that. In May Mik and I were descending from an ascent of the Freezy Nuts Couloir on Werewolf Tower in the Ruth Gorge. The climb had taken a bit longer than expected and Mik had run out of water. Just to be clear, he's tougher than I am and could have easily just continued down and drank his fill when we were back at camp. However, there was no need for him to remain thirsty.
We had paused for a break in the downclimbing at a flat spot below a small rock band. The rock band was running with water from snow melting above, but it was just a thin film of liquid. A simple trick allowed us to fill Mik's empty bottle with about a liter of water in just a few minutes. He pressed a dyneema sling onto the wet rock. This conducted water directly into his bottle.
Obviously this was a fairly hands-on operation. If we had more time, wanted to collect more water, or wanted to multitask we could have placed some gear in the rock, clipped the sling to it, and set the bottle upright in the snow with the end of the sling inside. Quickdraws or a cordelette could also be used for this task, and could be clipped to each other if more length is required.