As has been said, retraction braking on a fixed gear aircraft just makes you feel more in control, but has no engineering reason behind it.
On transport category aircraft, most type have a feature called retraction braking, that applies the brakes to stop rotation before the wheels are fully up. Typically, the de-rotation happens over 2s or so whilst the gear is travelling. The principle reason for this feature is to prevent a burst tire retracting into the bay whilst spinning and allowing the tire to damage hydraulic lines, fuel tank walls and anything else in proximity etc. Gyro effect is also a consideration but given the wheels are still spinning at the start of retraction this feature does not help so much.
The reason the brake application is limited in torque (typically to a reduced psi for hydraulic brakes), is to reduce the loads on the gear during the braking itself. These cycles have to be taken into account when calculating the fatigue spectrum for the gear. High loads = lower total gear cycles or beefier gear.
For the nose, a snubber may be used to stop the wheels in the bay or they are left to spin down naturally - there are less critical systems in the NLG bay compared with the mains.
Alex