Why is the landing gear lever not set to OFF on the ground? Several older airliners (e.g. Airbus A300, Boeing 737 until the NG series, Boeing 747 until the -400 series) have landing gear levers with three positions: UP, OFF and DOWN. OFF (or NEUTRAL for Airbus) means the hydraulic pressure is removed from the system because the gear is held in place mechanically. See also Why does the landing gear control have 3 positions (up/down/off) on Boeing 737-800?
The gear lever is typically set to the OFF position after the gear is retracted during the takeoff and the system therefore remains unpressurized during the flight:

Pilot Monitoring After flap retraction is complete:
[...]

Set the landing gear lever to OFF after landing gear retraction is complete.


(Boeing 737 NG FCOMv1 NP.21.46 - Normal Procedures - Amplified Procedures)
The gear is then lowered by selecting DOWN before landing, but it is not selected back to OFF after the landing gear is extended. I can understand why this would not be done during the landing phase (redundancy by keeping the gear pressurized down, reduced crew workload during highly critical phase of flight), but why is the lever not selected back to to OFF after landing?
Every procedure I can find lists the gear lever as DOWN on the ground:

Landing Gear Lever:

Check the L/G lever DOWN and the EMRG retract pb protected.


(Airbus A300 FCOM - Cockpit Safety Inspection)

LANDING GEAR lever .....................................................................DN
Verify that the green landing gear indicator lights are illuminated.
Verify that the red landing gear indicator lights are extinguished.

(Boeing 737 NG FCOMv1 SP.6.1 - Supplementary Procedures - Electrical Power Up)
Hydraulic pressure is not required to keep the gear down:

Landing Gear Extension
When the LANDING GEAR lever is moved to DN, hydraulic system A pressure
is used to release the uplocks. The landing gear extends by hydraulic pressure,
gravity and air loads. Overcenter mechanical and hydraulic locks hold the gear at
full extension. The nose wheel doors remain open when the gear is down.

(Boeing 737 NG FCOMv2 14.20.2 - Landing Gear - System Description, emphasis mine)
And furthermore, hydraulic pressure is lost anyway once the engines (and electrically powered hydraulic pumps) are switched off on the ground. So why would you want to keep the gear pressurized down on the ground until shutdown and again during startup?
Because there's no advantage to doing so (since the pumps will soon be off anyway, as the question notes), and this would create the risk that the pilot may overshoot the Off position to the Up position, which could, on a bad day, lead to an inadvertent gear retraction and major damage. The over-center locks are good, but do you really want to bet big bucks that the combination of 3,000 psi + a bad bump in the pavement will never produce an illustration of Murphy's Law?
Okay, there is one other safety to prevent overshooting, but that solenoid can fail, and if it does, watch out! There is simply zero need for this.
Also, depending on the plumbing, you might remove hydraulic pressure from the nosewheel steering by doing this (though I'd have to check the diagram to be sure).