A writer asks if they should "cover the brake" when approaching an
intersection.

Sounds like a bad intersection design. If you don't have visibility to
see a vehicle approaching on the cross road to make your go/no go
decision then the posted speed is too high. Or your scan pattern is
faulty.

Green, to me, means the driver has to "clear the intersection". The
driver has to visually sweep the approaching roads to avoid crashes.

A signal implies visibility of cross traffic. Otherwise the
intersection should be controlled by two way or four way stop signs.

Or better yet, a roundabout or a flyover.

Speeds are set at the 85th percentile of observed speeds. Drivers
adjust speeds for congestion, but not for sight stopping distance. Or
consent relative bearing crashes.

Yellow signs versus white signs.

This intersection sounds like it needs some engineering corrections.

To me, covering your brake means to put your foot on the brake and even
actuate it to the point of lighting the stop lamp, but not actually
forcing the pads onto the rotors. This saves maybe 200 milliseconds,
about one half car length at 40 MPH.

If you are trying to control your car to the nearest half car length at
30 MPH, you are way over the control limit of steering or braking. You
are very likely to induce steering oscillation and overturn your car if
you try to steer fast enough to miss the approaching car. At thirty
MPH, you should allow a cushion of at least three car lengths. That
includes the approaches from the sides.

Give yourself more cushion. One car length for each ten MPH up to 30
MPH then two car lengths for each ten MPH over 30 MPH.

Approach speeds are nearly equal in your example. Thirty and forty MPH.
Angle of constant relative bearing, about 50 degrees for the slower car
and 40 degrees for the faster car. The driver of the slower car MIGHT
notice the faster car if he moves his head and eyes. Neither driver
will see the other car if the cars remain on a constant relative
bearing and the drivers don't move their head and eyes. Or if there are
shrubs, trees or buildings in the line of sight.

If you are covering the brake in anticipation of the light turning red,
you need some practice on solving the dilemma zone.

There is a segment of road on the approach to a signal where you can
either proceed before the light turns red or stop safely, even of you
still have some yellow.

At some point in the approach to the signal, you need enough confidence
to stop looking at the light. Not because you know you are going to
make the green, but to scan for other vehicles. If you concentrate on
the light all the way to the cross bar, you will not see other traffic.

For most intersections, the solid lane divider gives a visual clue. If
you are at the speed limit to about 5 MPH below and the light is still
green when you reach the solid line, your car will enter the
intersection before the light turns red. Don't speed up, don't slow
down. Look for cross traffic.

Next time you are a passenger going through that intersection, notice
how much of the cross road you can see. Can you see the cross road
through the side windows? Or is anything beyond the A pillar blocked by
shrubs or signs?