I think I've been unclear on the problem. Trust inside a single team is not something I've found to be a major problem, but between teams. Let's be more concrete:
I need to build trust between between 6 EMs spread over three different directors and 2 vps + some very senior engineers. I need to do this so that we can solve one of the larger problems the business is facing. Most of these people have no good reason to talk to each other (or me) regularly. Without trust, one or more of these people will likely torpedo the proposal in order to avoid tying themselves to other teams and people they don't know.
Pre-covid the solution to this problem was (mostly) chatting over lunch. You'd get the right people talking, seed the idea, and build up to a proposal that everyone could agree to drive forward. IME this whole style of consensus building is dead in a remote world because async communication is too low bandwidth for trust building.
This makes it really hard to take good organizational bets, you have to wait till you have a mountain of data and customer feedback before you can sell big projects. The quality of the company's output really noticeably declines from this.