Is it okay to assign free marks for students assignments?
This heavily depends on your country, institution and position (most professors can get away with everything in regard of teaching if they research well).

In my country in Central Europe, this strategy is in universities not unheard of (because of the arguments you mention). One of my high school teachers even claimed that she is not allowed to give marks about the content of the homework, only about whether we did it in time, read the assignment careful and wrote comprehensively.

Of course, you could also make the homework weigh less.

Personally, I like this approach if you not mark the contents but whether or not they tried the tasks in a reasonablr fashion.