Does it make sense to reward the entire class with better grades if (and only if) no cheating is detected?
The problem with your proposal is that, despite you framing it as a reward rather than a punishment, it is trivially easy to reframe it as a punishment instead of a reward:
&quot;The exam is graded out of 47 points with three bonus points, unless someone tries to cheat.&quot;
is just as valid as:
&quot;The exam is graded out of 50 points but will only be graded out of 47 with three bonus points if no one cheats.&quot;
And I am entirely certain that many disappointed students who aren't the ones involved in cheating will reframe it as negatively as possible.  And no one likes collective punishment, because it isn't fair.
I've certainly noticed an uptick in cheating, as has my department.  I've tried to be proactive, and it seems to have helped.  Rather than just putting my academic integrity policy in the syllabus and talking about it on day 1, I involve it more directly.  For example, my first homework always comes with a quiz on my classroom management portal, that they get full credit for just for completing.  It asks questions in a way that I designed to make it more personal.  Things like:
&quot;One of my friends is struggling due to real-life reasons, and can't keep up with their work.  Out of a desire to help, I share my work with them, and they copy it.  What will happen?&quot;
I've only completed one class with these sorts of warnings, and my sample size was small, but that class did better than my previous class.