> Are you sure?
Yes.
It's pretty confusing, I did the same thing and came up with the same answer as you. Then I typed a sentence about "even on fully independent multi-link rear suspensions" before going off into the weeds. If the suspension were rigid, it seems like it should do the opposite, climbing upwards, but there is more going on in the car than the assumptions we typically make with a model.
A rear suspension is of course not rigid. It is, in short, a vertical damped spring mounted on a lever attached to the frame in front of it's axis. The axle/wheel hub is attached to the bottom of this damped spring at the end of the lever.
During braking, the rear will deflect rearwards and also be drawn towards the centerline of the vehicle following the arc of a circle drawn on the ground. The suspension will control the forces through the trailing arm, directing them towards the rear along a second arc drawn on the side of the vehicle, centered on the rotational vertex where the trailing arm is bolted to the car in front of its axle. The sway bar will control both sides to the same level which will be the apogee of the circle, closest to the rear bumper.
You can test this by pulling your parking brake below 5mph. If this doesn't work, call your mechanic :)
>You can't easily compare because the rear wheel easily skids with a fraction of the braking force the front wheel can take.
That is because braking the front bike wheel causes the lever to apply an upward force on the rear axle, pulling the front wheel rearwards, causing absurd instability and poor handling. This also happens to the rear wheel, it wants to hop upwards in response to the brake forces. That's why the proportional brakes exist in highway vehicles, to stabilize the braking forces into the most efficient braking scenario. If the front wheel were mounted in a reverse mounted trailing arm suspension (This doesn't exist, so I don't know what else to call it.) it would drop the front of the bike as happens to a car instead of flipping you off the bike. The side effects of this are atrocious understeer and a nonsensical center of gravity.
The reason the wheels move like this is to control for a characteristic called caster. Bikes have negative caster, if you let go of the handlebars at low speed, they will flop to one side or another at random, causing you to crash. Cars have positive caster which is the most stable configuration for the steering to operate. This is also why your steering wheel returns to center when you let go of the wheel while moving forward, and it is why the braking forces can be stabilized in this manner.