Say Woodley is making $10m this year. We ask him to cut to $6.5m. We let Worilds walk, draft a young replacement (maybe a $2m or $3m), and move forward. Go the other route now. We sign Worilds. Let's say we get off cheap, at $8.5m a year. We eat a portion of Woodley's contract, cutting him outright. Maybe that is $5m.
These numbers are all hypothetical (I don't know the particulars), but in the first scenario, we have tied under $10 to that position. In the other scenario, we have approaching $15m, and we are stsill in a similar situation (relying on an injury-prone guy... both Woodley and Worilds can't stay healthy). In the former scenario, at least we would have a young replacement waiting in the wings.
The other knock on this whole scenario, is that spending a high pick on another OLB takes away that choice that could be used at another position.