Minus the thing about pumping freezing air into a computer where it will condense and fry everything, is there a reason other than the noise why a big fan like this couldn't effectively cool a computer?
when it goes below zero C outside, moisture content drops to 0%. with enough static pressure to keep the inside air out of the case it would be completely fine.
we had a long-running research project on this very thing at uni, they basically built a data center with no walls and ran it all through the winter. no damage, although they did have to periodically brush the snow off the servers so they didn't get too warm due to airflow restrictions.
If done right no, there's no reason other than noise, size, and power usage. It also might pick up small things which could impact the components if the fans are strong. At worst it may push them out of place. That last two are pretty unlikely though.
It my be hard to ensure airflow as small pockets of a may form due to turblance that can't exit the system however.
All in all though there's no reason why a big ass fan couldn't work and if airflow to the heat generating components is right it would be better at cooling
Pointing a desk fan into a computer works fine and is a useful troubleshooting step if you suspect something is overheating, but if you need to do it that probably means heatsinks are clogged with dust, aren't sized appropriately or aren't making good contact. So you really should fix that problem.
PC fans are very cheap though, most aren't $700 but even if they were, old decommissioned computers are cheap or even free an the fans in those will likely work well enough anyway.