Why not a Quad Tiltrotor Pusher-Puller?

I haven't looked much into the future design of the quad tiltrotor, if
anybody else has, please post any info you can. But a quadtiltrotor
seems to be a promising project. I presume the engines in front and
rear would be standard forward-facing props and I guess they would be
offset so that the rear props would be pulling "fresh" air (as opposed
to air which was already pulled by the front props).

My question is why not configure the rear engines as pusher engines?

Did the German Arrow aircraft not show that this was an effective
combination?

Wouldn't that somewhat alleviate the need to offset the engines/props?
It would certainly space the props further apart.

Disadvantages:

I would guess the main obstacle would be the ground configuration of
the aircraft. Since the rear props would be pushers, they would have
to be pointing down for VTOL. How would the landing gear be
positioned so that the A/C would be balanced properly yet not
interfere with the rear props spinning rather close to the ground? I
can't answer this question off hand, but suspect there might be a
solution.

Another disadvantage would be the rear pusher engines could not tilt
much while on the ground. Since the rear props would be dangerously
close to the ground, tilting them a few degrees would put the front
blade tips very close to the surface. So the rear engines could not
help much in a STO. An STL (I don't know if the current tiltrotor the
V-22 Osprey even does this) would be impossible as the bouncing around
and any yaw or roll caused by any variation in ground surface would be
very dangerous with the rear props so close to the surface.

The aircraft would have to be longer than a quad-forward-facing
tiltrotor. Since there is more distance between the front and rear
props, the tail would have to be set further back to keep it out of
the way of the props.

Yes there are lots of practical disadvantages, no doubt many I haven't
listed. But I bet a quad pusher puller tiltrotor would cook in
airplane mode

It would be interesting to see the effects of transitioning from
airplane to vertiplane mode. I wonder if all four engines could
transition at the same time or whether it would be better to rotate
the front two by themselves before starting the rear to rotate. I
would guess all four engines would have to rotate at the same time as
otherwise there would be an imbalance of the vertical lift.