I used to do the same when I did software development “I will be done with that in 2 days” then proceeded to build the thing in 2 hours chill 3-4 hours and hand it in earlier than expected. Everyone was happy.
Additionally as another case, Hubble has been continuously losing gyroscopes since it was first launched. Some or all gyros were replaced during most shuttle servicing missions. Seeing the writing on the wall for servicing missions post-Columbia, NASA developed software to operate with fewer gyros at a time, allowing for fewer to be spun up at any time, but importantly, allowing for the telescope to continue to operate after more than 3 of 6 gyros had failed. The key here is that engineers can often coax more performance out of a damaged (or otherwise limited) subsystem given the incentive- this has been the case in my aerospace experience, and seemed mirrored with Hubble too.
I think that's an unnecessarily pessimistic take. Any system can have its life expectancy modeled over a range, e.g. a 99% chance it will survive 1 month but only a 50% chance it will survive to 1 year. When you're just giving one number to the media or other stakeholders, e.g. "expected life span", (or, for that matter, a single estimate to your boss), to be able to give a value with high confidence you will have to pick a number that is in the 99%-ish range, which means there is a good chance your system will survive much longer.
As to your related point, I probably wouldn't use the term "scared." But, yes, there are a lot of incentives to meet/exceed goals and strong disincentives to fail by not meeting a somewhat arbitrary lifetime of a probe. Of course, some probes have clear primary objectives and you want to hit those but you may not want to "promise" you can hit a bunch of less important secondary objectives as well even if you think you probably can.