All contestants on all game shows also sign a contract saying that all decisions of the judges are final. That doesn't mean the judges (who are usually the producers) can expect to do whatever they feel like irrespective of all the other rules and think they'll get away with it. Even a contract with clear, iron-clad language can be invalidated in court if a judge believes it is "unconscionable."
To reasonably enforce a time limit, the parameters need to be clearly established ahead of time. Not all rules have to be explained on the air. Even the specifics can be a little loose. Richard/Ray got to start the 3-second clock on Family Feud whenever they felt like it, BUT it was always 3 seconds, and they couldn't buzz a non-answer without invoking it. All of this was explained to the contestants before air. Producers who make up whatever limitations they feel like on the spot are asking for trouble.
I get what you're saying about not calling an audible for a specific contestant--I'm just saying the Millionaire producers were more willing to let Regis loose. There were limitations, sure, but they were still willing to give Regis more trust than a host normally would get. (None of the other hosts ever attempted to probe as deeply as he did, although they do get involved to a degree.) The tradeoff was they had to take precautions to keep their host mostly excluded from other production decisions.
But if the showrunners can't secure Regis' privilege to pick a contestant's brain about their thought process--
there's no show. Otherwise the viewer has no idea what the contestants are thinking. All you're left with is a nervous contestant staring at a monitor, and that'd be
deathly boring.
Or on the opposite extreme--if you have a crazy gambler like Norm Macdonald in the Hot Seat, you need the latitude to poke and prod and let them expose that they actually are are not trivia experts but massive risk takers. Norm's $500K and $1M questions are some of Regis' most memorable moments, precisely
because Regis is clearly exasperated by Norm's reckless gambling. He even tries to interject and begs Norm to reconsider when Norm's clearly about to just guess on the $1M. But once Norm says "Final Answer", there's nothing Regis can do. It's Norm's mess, he has to own what happens. And it's obviously driving Regis insane--he's clearly doing all he can do to help out, up to the very limit, but Norm was having none of it. (I friggin' love it, one of my favorite hosting moments)
(start at 21:25)
Now, Millionaire
definitely pushed it, probably more than any other show before it would ever be comfortable doing. And not every show has an industry veteran like Regis at the helm, so I wouldn't recommend they try. But it was something magical to see, a far cry from some of today's shows where the host repeats the exact same patter every day, and any "get to know you" questions are just a vehicle to get to the next scripted rule explanation the host has to repeat.
In either case, the host doesn't have a gun to the contestant's head, and as long as the contestant is aware of limits like
1) the host doesn't know the answers
2) the contestant can't ask the host for help
3) the host is aggressively trying
not to "help"; the host may not favor or disfavor a particular contestant
4) the host's job is to make good TV by picking the contestant's brain and building drama, not by helping or hindering
5) the contestant can dodge the host's questioning with non-answers if they feel it is in their best interest to do so
then I see no issue with giving the host a little latitude to pick a contestant's brain. Just as long as they give the same amount of latitude to
all contestants, of course.