The answers are as varied as the tournaments themselves. We (Tucson State) just recently switched to electronic bout cards and while we love it now, it wasn't an easy transition. You need computers and, more importantly, a solid WiFi system with redundancy (unless you run ethernet, which also presents challenges). We had triple redundancy last year in Prescott and still had issues because the ISP provider's system went offline temporarily and simultaneously, the AT&T hotspots we had, slowed to a crawl due to the increased traffic. But...with the presence of Chromebooks these days...it only makes sense to go paperless and I would encourage any tournament to do so - it is worth it!
We always liked the paper backup but to be honest, I am not sure it truly gets you anything the e-boutcard doesn't. In almost every disputed case, the wrong winner was circled and I have never had an opposing coach try to steal a win because the boutcard was wrong - ever. If its scoring, you can just as easily compare the boutcard to the two books and sort it through.
It takes a heck of an effort (and dedication) to run a tournament, especially a large one, and it generally isn't the only thing on their plate. So...once you get a system down (like printed boutcards) it is comfortable and easy to stay with. The old "if it ain't broke, don't fix it" mentality argues in your head against adopting and risking change because if it doesn't work, you fear that you could "break it" and make it worse! Does that make sense? Not the most satisfying answer, I know, but probably closer to the truth than just about any other explanation, given my experience.
Finally, I think if you offered to help at a tournament to improve it, someone would take you up on it, especially one ran more locally and without the infrastructure that the larger tourneys enjoy. You could be part of the solution that we definitely need in the state in terms of our wrestling tourneys. But who knows...I offered an easy script that uploads updated documents (think brackets) to a website to Peoria a few years ago so that people could stay updated on their results...and never heard a thing. That offer still stands...as well as anything else I could do to help any tourney.