Absolutely - the risk of re-ingestion and FOD is primarily related to airspeed, not ground speed.

What is your airline SOP,?...rev thrust or braking?

Aside from all of the FOD risks noted above, this is an engine cycle that is counted for maintenance. Most airlines tend to want to reduce rev thrust cycles and time, to reduce maintenance cycles on the engines.

Brakes/replacement are far cheaper than engines.....

Yes, but more than one airline found that the money saved was negated by some order(s) of magnitude by having an aircraft off the end of the runway in the greenery.

We're to be fully out of reverse by 60 kts.

As many have mentioned, you risk FOD ingestion keeping them out leaving the runway.

I dream for a day when fleet managers stop making up their own procedures.

I've seen a handful of mostly corporate types with high tail mounted engines using reverse on taxiways to manage speed.

That you'll be slowing to a safe speed before turning, is the type of obvious and unnecessary statement that we should not be clogging frequencies with. Like that we won't be taking off overweight or flying slower than stall speed. Duh.

ATC should know that planes have to slow down more for turns when it's slippery out; and if they don't, they'll figure it out quickly enough.

At least in the Boeing world, most of what you wrote is simply wrong. Deploying the reverser is not counted as an 'engine cycle' - only a takeoff is counted as an engine cycle. Max reverse N1 is significantly lower than max climb, so it's not really taking anything significant out of the engine, and FOD damage risk is almost non-existent above 80 knots. It is counted as a reverser cycle, but the Boeing MPD tasks assume one reverser cycle per flight cycle so in most cases you'll be doing the reverser maintenance regardless. According to the Boeing R&M types, appropriate use of the reversers on the 777 saves ~$100 per landing in total maintenance costs (not to mention the costs of going off the end). Brakes aren't cheap either.
If you respect the FCOM recommendations on reverser usage - getting them to idle by 60 knots, and stowing by taxi speed, the risk of re-ingestion and associated engine damage are minimal.
The key is to respect the FCOM recommendations - reverse below 60 knots doesn't do much aside from killing the forward idle thrust - so there is really no reason to use them unless getting the aircraft stopped in time is not a sure thing (in which case abusing the reversers is probably preferable to abusing the airframe).

While training crews in Asia who were used to their company procedures (not necessarily Boeing FCTM procedures), it was noticed they tended to completely cancel reverse thrust at the 60 knots call during the landing run. At the call of 60 knots, they would slam the reverse thrust levers fully down from full reverse (Boeing 737). This would cause the aircraft to momentarily accelerate down the runway while the pilot was still also applying the brakes. The reason being the N1 would be still running down through around 60% N1 when the reverser lights went out; thus giving momentarily significant forward thrust.

It wasn't until the English second language pilots were advised to carefully read (and understand) the FCTM instructions about the need to allow the N1 to reach idle reverse before cancelling, that the penny dropped they were doing it all wrong.

It got me thinking about landing with loss of all hydraulic braking capability - rare though that possibility could be, of course. The scenario in the simulator was concerned with the use of reverse thrust and the aircraft managing to stop still in full reverse right at the end of the safety area with a nasty drop at the end. How do you cancel reverse when stopped without the residual forward thrust inherent with cancellation from full reverse, trickling the aircraft over the cliff?

OK - I confess it is a bit far fetched but sometimes a bit of lateral thinking doesn't do you any harm; especially if there is nothing in the book about such a non-normal. And neither does there need to be.

Answer? At the moment the aircraft stops right at the end (your lucky day) cut both start levers while the engines are still at full reverse. With a bit of luck, there will be little or no forward thrust to roll you over the cliff with no brakes.

Writer quickly exits stage left..

Or just go to idle reverse and let the plane back up a before cancelling

Had this happen in a light jet, Citation bravo. Has a seperate hydraulic system for the brakes and we lost all the fluid. I diverted to the longest runway, used the reverse to slow down to a complete stop. I had my hand on the emergency nitrogen powered emergency brake in case I needed it but wanted to avoid using it if I didn't have to because of the extra maintenance. So after I stopped I felt it started moving backwards, so I selected forward idle on one of the engines, stopped, shut both down, and we stood still long enough for the fire department to chock the nosewheel.

Quite a while back, some airliners with tail mounted engines (DC-9/MD-80, 727’s, certain Fokkers) routinely used reverse to “power back” off a gate to save cost of having extra tugs. I think someone eventually figured out that the cost of fuel and wear on the engines was more than the cost of the tug.

If you do not stow the reversers upon reaching the taxiway you risk ingesting FOD and other stuff, as an A319 crew found out when they exited the runway in wintery conditions with the reversers still deployed. The low swung engines ingested de-icing chemicals, which caused smoke en fumes in the cabin, which led to an emergency evacuation initiated by the cabin crew (!).
Report: Easyjet A319 at Belfast on Jan 6th 2011, taxiway de-icing prompts evacuation


Anyway, Airbus FCTM says: stow reversers before leaving the runway to avoid ingesting FOD. Seems pretty sensible to me.

Is that the manufacturer's recommendation? Depends on aircraft type. For example B737 FCTM states: "Maintain reverse thrust as required, up to maximum, until the airspeed approaches 60 knots. At this point start reducing the reverse thrust so that the reverse thrust levers are moving down at a rate commensurate with the deceleration rate of the airplane. The thrust levers should be positioned to reverse ideal by taxi speed, then full down after the engines have decelerated to idle. Reverse thrust is reduced to idle between 60 knots and taxi speed to prevent engine exhaust re-ingestion and to reduce the risk of FOD. It also helps the pilot maintain directional control in event a reverser becomes inoperative. The PM should call out 60 knots to assist the PF in scheduling reverse thrust."

You can't get it more clearer than that.