The Time and Expense profile users in Core cannot see the cost rates in the Expense Entries screen.
This is by design. Show Cost and Show Cost Amount security permissions are interdependent. If both are enabled in the Security screen, then both values will show up on the Expense Entries screen, but if either of the two is disabled, then nothing shows up on the screen. To address this issue, you need to turn on both permissions, save it as a new Security Profile, and assign that profile to all current Time and Expense profile users.