For what it's worth, I live in the northwest U.S. Forestry is critical to our ecosystem here, and it's an ongoing treadmill to keep the forests from becoming overdense. So, around here, paper is quite good for the environment, because it's a good use of a resource we need to heavily thin anyway! (An overthick forest is a burning forest.)
That aside, you can do desk checking without printing, as you've described, but I think it needs to come back as a practice in some medium at least.
Also, if you make a mistake building a wall, the wall falls over. If you make a typo in a piece of software, the results range from a minor inconvenience to a lost satellite, from a screen flicker to a catastrophic, fatal plane crash. We should NOT be downplaying the seriousness of bugs.
Now, that said, there are some differences between engineering fields (sciences) and programming (more of an art than a science). Where the comparison is apt is still in the tools. ;)
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