A logo? Remove the automatic part and focus just on the deliverable; whether it's made by a computer or by a human, what you get is a few concepts before you select the one you like. And then you go with a lawyer to protect your IP.
Which makes this way more expensive than a normal logo created by an actual artist.
If I contract someone to make me a logo, I can normally safely assume there won’t be lingering IP issues after I have the deliverable.
This clause is not about copyright on the logo itself. It's about trademark law and all the difficulties therein.
I understand your concern about copyright. In copyright, the source of the image is what matters, not its appearance: If you created your own logo that happens to be similar to an existing logo, but did not actually copy the existing item (and could prove that), you'd be fine. If you did copy it, and made significant changes until it didn't look confusingly like the original, you'd be guilty. But this isn't the problem that "perform due diligence to determine that the use of the Design Resources is free of any adverse claims and is not subject to any third party rights" is warning you about.
Trademark law is different than copyright law. If you create a brand new logo that, unfortunately, happens to look by random chance similar to another logo that already exists in your market but you didn't know about, that's an IP issue. You need to search out and differentiate your logo from all conflicting logos that already exist.
This search is why no artist or automatic logo generator could guarantee that you're able to use the outputs.
Unless I'm missing it in the terms, the user isn't even clearly allowed to use their designs as the basis of a known-safe design, since they don't explicitly permit changes to it?
When talking about the finished logo, they talk about "End Products".
They define "Design Resources" as
Throughout the process LogoFox will also make use of certain symbols, colors, fonts and other design elements (collectively known as "Design Resources”) [...]
and then state
d. Third Party Design Resources
[...] All use of these Symbols is AT YOUR OWN RISK. You shall abide by all copyright notices, trademark rules, and shall not use, copy, reproduce, modify, translate, publish, broadcast, transmit, distribute, perform, upload, display, license, sub-license, rent, lend, assign, gift, sell or otherwise transfer or distribute for any purposes whatsoever any portion of the Design Resources not owned by you: (i) without the express prior written consent of the respective owners or (ii) in any way that violates any third party right.
You acknowledge that some fonts and symbols used during the Design Process might have been licensed from a third party provider. Under no circumstances will LogoFox be liable in any way for any Design Resources, including, but not limited to, for any loss or damage of any kind incurred as a result of the use of any Materials or any part thereof.
Delivering a design where you can't even tell the customer about the license of the fonts you used is... weak. If you want to offer cheap designs, use open fonts or clearly tell the customer where they can get their own license, don't just let them figure it out themselves.
It is literally impossible to vet an idea / logo / website name, before you even have it.
First you design, then you apply for protection.
