That was not what the President was talking about though. I'm sure that the President is fully aware that Starfleet Captain will at times needs to make the ultimate sacrifice. But this wasn't one of those times. Rillak was specifically talking about Burnham being unwilling to delegate responsibilities to subordinates that may cost those subordinates their lives. This is actually a bad trait to have as a leader. Detmer or Rhys were probably perfectly capable of completing the mission and Burnham should have stepped back and allowed one of them to do so.
A good leader has faith in their crew and encourages them to take risks in order for them to develop experience. Everyone on Discovery's bridge know what they have signed up for and Burnham taking on all of the responsibilities because she wants to bring everyone home is doing her crew a massive disservice. Burnham needs to be sending the kids on dangerous away missions, getting them to do risky endeavours and putting their lives on the line, because as starfleet officers, they need experience in those situations. One day one of these officers, is going to need to make the call, and may find themselves ill-prepared to do so because Burnham chose to bubble wrap her crew instead of empowering them to take calculated risks.
Burnham also needs to realise as Captain that some times when you try to get no one killed, you run the risk of getting everyone killed. Part of the Kobayashi Maru test is to prepare cadets for that inevitability one day. If a Captain can't accept that some of their crew may day in the line of duty because of said Captain's orders, then they don't have any right being in the big chair.