Ok, why pay for a deliverable I might not be legally allowed to use, or might be associated with unknown follow-on costs to aquire that right? They are obtaining third-party resources somewhere, they would be in an excellent position to provide relevant documentation.
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?
Third party resources? The problem isn't the stock images or shapes the generator uses, the problem is you could create a logo for "Disney" here or accidentally make something too close to Blogspot's logo because your company name has the same initials and you like the rounded square shape that gets generated.
Read the section of the terms of service being discussed. It's about "third-party design resources" and how you are using them at your own risk, not about a general guarantee that the logo isn't conflicting with an existing trademark etc.
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.
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?