It probably takes a different type of academic to do replication studies. It's a specific kind of detective work, to see if you can expose someone else's mistakes which are sometimes even deliberate.
We need more of this type of people.
EDIT: In addition to this, perhaps we should stimulate new students to do a replication study as part of their education.
Imo. this would actually be a great target of public funding. A large international research organization with the the sole purpose of replicating, validating and criticising existing research.
As you correctly point out, the skillset is slightly different to doing novel research, the attitude is different as well, so it would make sense to pool talent. Since there is no money to be made directly with it, governments should step in. And to avoid the problem of journals not wanting to publish replications, the institute would have to be well funded enough to self-pubpish with prestige.
We need more of this type of people.
EDIT: In addition to this, perhaps we should stimulate new students to do a replication study as part of their education.