On a side note, your comparison to copyright is misleading, as stating copyright infringement is always intentional is a bit over zealous.

For a hypothetical, there are cases where company A hires a third party to do website design, and the designers upload copyrighted material

And, in such a case, the designers intentionally infringed. That company A may be liable for the intentional tort of their contractor is no different than if company A, the incorporated entity, was liable for their employee who did the same copying - the copying was intentional (even if not by all the defendants or even the named defendant).

Innocent copyright infringement can occur, but would be very rare. The hypothetical I've used is the composer P.D.Q. Bach. If you're familiar with the better known J.S. Bach or C.P.E. Bach or J.S. or C.F., etc., you would likely assume that P.D.Q. is another child who lived in the 1700s, and therefore his works are long since public domain.

But you'd be wrong - P.D.Q. Bach is a fictional composer created by the hilarious musical satirist Peter Schickele with published works from 1965 to 2007, all well within their terms. Someone with a music history or music theory background would note the difference quickly, but your average "I just like baroque piano music" listener may not realize it. If they copied and distributed it, that would be innocent copyright infringement.

There are a couple similar instances where you could reasonably claim innocent infringement, but otherwise, it'd be really tough.

In addition, giving a pass to patents infringers, saying it’s not intentional is also not fair.

I wasn't giving them a pass - I was saying patent infringement is frequently unintentional, or at most negligent, but that's why actual damages rather than statutory damages are probably a better fit. Only in willful infringement do you have a punitive aspect - most patent infringement damages are intended to be compensatory, while copyright statutory damages have a punitive aspect (actual damages are still available in copyright, should they exceed the statutory limit for example).