The answer to your original question is "trust the team". Integral to that is that they must have the skills on the team (or close to hand) to be able to do specialised work, in the same way as you might have someone with the "DBA" job title who specialises in databases. What you would expect is not that all the database work goes to the DBA, but that other team members would pick up DB jobs that don't necessarily need the full depth of their skills, with the DBA there to help if needed, and the team would be able to sort all that out themselves without management overhead. Incidentally that's also why you don't need to hire people who already have cross-cutting skill-sets. You're aiming to hire people who can learn, and trusting them to do so.

If you're not in a situation where you can envisage "trust the team" being something you could live with, then yes, what you're doing probably looks rational to you. "I can't spend my dev hours..." makes me think you're in a fundamentally McKinsey/Taylorist environment, low-trust by design. That's not uncommon, but it doesn't make other approaches wrong either.