When people talk about the core, it's about them as a unit and their impact on the team's cap structure in relation to their playoff performance. If you keep running the same core pieces at their current cap hits, you will get the same results regardless of what's around them.
It's the reality of the cap space available to fill out the roster.
In fact, you sort of mentioned the effect of this in your post. Since they have no cap space due to the core guys, they keep adding cheap "dead-weight" players that come with issues, sign one-year deals not allowing for long-term chemistry, or aren't good enough.
The only way to resolve this is with cap redistribution.