I'd rather leave it as it is, but there is definitely an argument for it. It wouldn't surprise me if it's brought in ala goal-line technology after something like the following happens in a big final.
I too am a "Yank", and one that has lived here for almost 28 years.
The vision above (thanks for the great memory BTW jimbler) is exactly why I like not having a clock.
Those likening having a time to end of game displayed to the stop\start nature of the NFL clock needn't worry as this is better compared to the clock stopping and time on TBH.
Still the subtle nuance of not knowing exactly when time is up forces changes in players mentality on whether to hold or move on quickly and like I said, I'm a fan of not showing the time.