It's not illegal perse but without a license file all rights are reserved to the owner per GitHub. So you could get sued and they'd (maybe) have a case.

I won't argue for a particular license, but you should have one. I personally won't touch a project without a license as I usually aim to monetize my work somehow and don't want a potential legal headache.

For example in Germany. Copyright applies automatically and you can't just use anything (images, code, text, and so on) without explicit okay by the producer of this.

A license just allows you to use the content/code under specific conditions.

Else you just are not allowed to use it.

AFAIK in at least some countries it's enough to mention the license somewhere. It's not necessary to include a full license file.