You're quoting Delta, one of the most restrictive of all the airlines when it comes to flying with bikes. So sure, you could lose your ability to get the cost of the bike back if you don't claim it. But....

In all my travels, I've never lost a folder. I refuse to live in fear that I will, I don't fly Delta anyway, and while it's certainly possible that my folder will get lost or stolen, my extra efforts at leaving all kinds of contact info within the suitcase make this possibility remote at best. After all, there is a certain freedom in flying with a bike as checked luggage and being able to use said bike at the destination, dovetailing with public transport wherever you want to go. One of the reasons I got into folders in the first place.

So if you want to not fly with your folders, feel free. The OP asked for advice and I gave it. Not interested in raining on his parade, and I hope your admonishment that you might not get your bike back and/or be compensated for it doesn't deter him from flying with it.