The crew chief is the one talking to the strategy team and juggling the cars. They actually implement the strategy so they're quite aware of it. As you noted, they've got the ability to screw it up as well. Ever had to make the call at 7 AM, 19 hours into a race, as to whether you should take the time to do a brake pad change or not? That's not a matter of just sending it, that's a matter of evaluating just how fast you're using the brakes and what you think your lap times will be if you do or don't. That decision comes after hours of measuring pad wear at every fuel stop. Or maybe one of the team cars has just rolled at dawn and it has the only good remaining transmission in it, do you call in the car with the bent shift fork that can only use 4th gear into the pits so you can do a transmission swap? The answer to the former was "yes" and it won us the race. The answer to the latter was "no, because we'd lose time overall even though we'd be able to go faster".
Other jobs? Mechanic, fueler, car builder - and this is for pro or semi-pro Thunderhill 25H teams, not Lemons. I've also been a rally driver and team principal on week long rallies, there is a lot of strategy there as well as to when to push and how to manage the limited number of tires.
If you think it's just going fast and leaving nothing on the table, you'll lose to someone who's playing at a higher level. The trick is to drive just fast enough to finish in a shorter overall time than anyone else. Some of the classic Le Mans battles back in the day involved sending out a "rabbit" to force other teams to drive fast, leave nothing on the table and then break. The rabbit isn't expected to survive, but it pulls the other team into an undesirable strategy. Ferrari pulled a good one this past weekend, that pit stop on lap 27 forced Mercedes to choose between two bad strategies despite having a car with faster ultimate pace. You can also nurse a car along at a slower speed if it means you maintain track position and cut your time in the pits - some of Lewis' best drives have had him eking incredible lifespan out of a set of tires. Remember the set of inters that he ran down to (terrible) slicks to finish first a number of years back?
