Are there any champions that don't benefit from mixing some ad items into their build?

Yes, pretty much any ap champion.

If you have ap ratios on your abilities, then building ap will give you more damage (and more burst, front loaded damage is better as it gets your opponent dead faster to stop their sustained damage).

Also, most tanks don't benefit as much from building ad as from building tank. They often have percent health damage (either their health or their opponents) and mostly deal damage from these abilities while living a long time to building full tank and using lots of crowd control.

Ap champion examples: and many more

Tank examples: etc....

Some tanks like or can and sometimes do build an ad item or two though (often of

Basically all AP champions. Sure a lot of them are ranged and can thus feasibly play like an ADC they generally much prefer having items. Same with tanks. If they build some AD then they lose out on a lot of durability.

Karthus is probably the worst champion to buy any AD on as his auto attack range is so low, his auto attack animation is terrible and his Q is on such a low cooldown that there's really never a point to ever use his auto animation for anything other than potentially last hitting when you're oom.

It not so much that they don't benefit at all, because any champion can and should try to weave auto attacks in between skills if possible, its more that the benefit of building something else is so much better that building an item with AD on it would hurt them overall in effectiveness.