I've never had a problem with "overuse." If there was an episode where he put it in his pocket and pulled out a different device to scan, it would not be any better.
Sure, the sixth Doctor didn't have a screwdriver... but when the plot required him to open a locked drawer in The Trial of a Time Lord
, he just pulled a different lock-opening device out of his pocket and used it.
It did get hilarious in the later Tennant era how many things could be "deadlock sealed" in order to slow the screwdriver down....