I don't believe the company can "request" a Captain to exercise discretion. It is called "Captain's" discretion for a reason. I would regard a request to operate into discretion as an unreasonable intrusion and have always considered it to be beyond their remit. It would be seen as exerting pressure. Fortunately this has never happened to me in a series of UK airlines.
This means that the company must assume that you won't be exercising discretion unless you volunteer it and should (must) plan accordingly. Failure to do so implies the assumption of discretion which is exerting pressure in an underhand way and is equally, and in some ways more unacceptable. This invariably happens which is grossly unprofessional on the part of the Ops Dept.
A minefield.
Check the wording in your Ops manual. It will say words to the effect of "to be used only in exceptional circumstances". To me that cannot mean every time or nearly every time it might be applied. It means it must only be used rarely. So your occasions of declining discretion should greatly exceed those of exercising it, else it isn't exceptional, it has become routine. (as is the case in every company I have worked for bar none).
Equally "exceptional" does not, imho, include events like general operational lateness which is manifestly NOT exceptional, it is routine. Force majeure, unexpected airfield closures (not due to forecast weather), medical delays fine. Wildcat strikes perhaps but late bags, late flight plans, late fuel, late pax, never.
The bottom line is you should seldom exercise discretion, and than only when all crew are genuinely fit to operate (as they always will be even when dropping on their feet at the end of a 12 hr 4 sector bad day and just want to get home). Fat chance!
I'd bet good money that not one case in 10 where it is used actually meets the criteria of "exceptional".
It is universally used - in my experience - as a "voluntary" duty-hour extension (and usually imposed by stealth) to cover normal operational glitches, which means it is universally misused.
Discuss...