There's no reason for Pike to keep quiet about what he's seen. At all.
It would have been better if, after L'Rell and Tyler ask Pike what he sacrificed, he said, "I don't remember, but I think it was something important." That would have worked with canon better.
As it is, Pike has no reason to stay in Starfleet for another 10 years. He knows something bad happens in a Starfleet ship. By all rights, he should resign after this Discovery business is over and never look back.
Since when did Pike become such a hardcore Starfleet cheerleader anyway? Just 3 years ago, in-universe, he was seriously contemplating ditching Starfleet to join the Orion colony.
Also, he would be required to tell what happened in his report to Starfleet Command. Although this is the same Starfleet Command that knew all about what would happen to the Defiant...
In any case, Dr. Boyce should come up and say, "Chris, I read your report, and you know what, your instincts were right after that Rigel mission all those years ago. Take this one way ticket to the Orion colony, and don't look back."