I understand logistically it might be an issue. It's that, watching the film, I understand much more now why they decision was made to kill Captain America after Civil War in the comics. Severing that ability to reconcile gives the events of their feud a permanence.
Even failing that they could have had Tony burn Steve's letter before reading. But to have him read it just shows that there isn't an impossible to cross chasm between them. They've already started the process of reconciliation.
Now that is just going too far. Tony isn't an asshole.