About 10 years ago, I read an article in (possibly) the now defunct Cricket Talk magazine, about a guy in Australia who built cricket bats with bent handles. The bent handle helped keep the ball down when driving, because the face of the bat was naturally angled downwards. Supposedly, a batsman in the Australian domestic shield (perhaps Simon Katich), even used it to make a century.
I am not familiar with the anecdote, however the laws of cricket state that the handle must be straight
It is a straight shaft for holding the bat.
From The Laws of Cricket.
On the other hand there doesn’t appear to be any restriction on the face of the bat curving and from personal experience and from watching games most modern bats seem to be curved, but in the opposite direction from what you suggest, i.e. the face curves gently towards the direction of the bowler when held in a regular batting stance.
One additional point is that I can’t see anywhere in the laws that demand that the join of the handle and the bat be straight, just that the handle itself be straight. However, from a bat construction and transfer of force between hands and ball perspective, you wouldn’t want to have anything other than a straight join of the handle and bat.
Anyway, these days everyone wants to play T20 and hit sixes, so this kind of design would probably not be popular even if it were legal.