> set the expectation that they have strong relationships with their own teams
Good luck with that.
In most cronytocracies (typical, at the top levels of most companies), you get who you get. They may be really good engineers and "first line" managers, but suck at anything else.
A big problem is that companies don't have career tracks that match people's skills. The Peter Principle[0] applies.
Bad managers hire and promote other bad managers. Highly skilled engineers can often be terrible managers, but want to be managers, because that is the position they equate with "success," at an organization.
A Principal Engineer should be just as valued and well-treated as a CTO. Most companies fail to do this, so everyone wants to be the CTO. Establish a career track, where technical people aspire to technical positions.
And hire good managers; not ones that don't make the CEO uncomfortable.