Patching is easy and effective if you know how to do it properly. Plus you have to find the puncture, which means you will know where to look on the tire to remediate the issue so your spare tube doesn't go flat 3 miles down the road. I carry a spare for a catostrophic failure (like stem breaking), but patching is simple,easy and a good skill to know.

Keep a couple cotton swabs in your pack/bag, use them to swipe the inside of the tube to check for additional debris/burrs while it is off (glass/wire/rocks/syringes will catch on the cotton).