Jim Cummiskey wrote:

Actually, no.

Actually, yes.

If you think about it ...

What makes you think I haven't?

... if you approach the numbers at a ~30
deg angle, and a "proper" downwind to base turn is made at a ~45 deg
angle,
there will be no conflict whatsover.

When you reach the point in your training where you start flying at
towered airports, you'll discover that there's no such thing as a
"proper" pattern. Downwind and base legs (as well as upwind and
crosswind legs) are extended and shortened for a wide variety of
reasons, to allow planes in and out of the airport effectively.
Especially when the airport is busy.

You'll also discover that there are larger, faster airplanes - some
even with jet engines - that fly larger patterns, and that can affect
(and can be affected by) traffic farther away from the airport. You
may have already discovered this flying around the pattern at your home
airport. If not, you may want to discuss this with your instructor
before he lets you solo.

Regardless, a plane flying "to the numbers" from 30 degrees off the
downwind side will cross every possible base leg to that runway.

It will also cross every possible downwind leg at some point. For
example, a plane on downwind set up for a 1/2 mile base leg could
collide with the inbound plane 0.866 miles downwind from the numbers.

On the other hand, if that inbound plane were to set up for a 5 mile
final, there would be no possible conflict for any pattern
configuration inside those 5 miles. That's a great reason for a tower
controller to ask for it.