For a team not used to code reviews, they might seem more trouble than they're worth at first. Most likely they will be more trouble than they're worth for the first few months. Keep doing them and eventually your smart developers will figure "if we have to do this anyway, we may as well find something useful to say" :)
A few things you can do to make it smoother:
- Manage expectations. Initially it may be as simple as "we just want to have a second pair of eyes on every change" or "be aware what other team members are up to" - i.e. communication first, improving code second.
- Set up your tooling to make the process smooth. If somebody wants to just get it over with - it should be easier for them to use your official review process then to use some side channel. A vicious alternative is to make using side channels harder ;)
- Leverage automation. Run tests, linters, static checkers, etc. on your PRs so that developers get something useful even if no human leaves interesting comments.
- If some team members already have experience with code reviews - adjust their workload so that they can do more reviews. They are effectively training others by example.
- Make sure that code changes under review are reasonably sized. Encourage submitting changes for review early and often. "Here is the feature I worked on for 3 months, and it's due on Friday, please review" won't make anybody happy.
- Make it less intimidating. Code reviews are not just for finding bugs and flaws, encourage reviewers to say positive things as well.