Part of hiring is finding out if someone can work well with a team. Lots of teams need everyone to be able to communicate well during collaborative problem solving sessions.

I've worked with the strong, silent type of coworker who has a solution in their head. But because they don't vocalize what they're thinking, I can't participate or help. That's not what I'm looking for in a good engineer and a good coworker.

It's not "good" versus "bad" engineer/coworker. It's a different way of functioning.

Some people (I'd guess introverts, although I'm not sure) need to internalize to think and can't interact much at this point. Some can think and discuss at the same time.

From these two sets of people, some can afterward verbally explain the reasoning and the solution, some can't. Some may also only require a context warm-up.

That makes 4 sets of people already.

"Technical" phone interviews that screen candidates that can solve whatever riddle, filter for a very specific set of people. Not necessarily the best in any context. But a specific set that works for them. Just admit/accept it.

It depends on who you already have in your team.

Having a few members who can solve hard problems on their own is great, and they usually have to be silent and focused while doing it. You also need people who are good at participating and helping and explaining their thought process. A team that has only one type isn't going to be the most effective team.

strong and silent is fine, as long as they are on the same page as you and you as them. It might take magic to do that. Communicating effectively is an important thing to avoid wasting time in red herrings.