It's really a referendum on the decisions the team made regarding the OL overhaul going back to 2011 (when Costa really logged his playing time after coming in as an UDFA in 2010). There was so much hyperbole about the early learning on the job he had to do when the team rolled the dice on letting Gurode go, and so much criticism of the overall direction (using premium resources on the OTs and trying to develop resources at the interior positions). The fact that the guy made the team, beat out the incumbent, got better over the course of a season, earned an extension, and then had his best games as a pro the following injury-plagued year in 2012 gets lost in the shuffle.
Like the lack of depth we had on the bench or not (I personally don't like how unprepared we were in 2010 for the required OL overhaul), to hit on an UDFA and get somebody capable of giving you starter's snaps was was fairly fortunate. But it fits better with a general narrative to pretend the guy is the worst starter we've ever had, and that it was reasonable to have expected him to come in with a college background at OG and convert to C and start the next season at C and not need reps to improve at all.
As a side note...was he actually cut? I see the story from two days ago that he was likely to be released, but can't find confirmation yet. Given his salary right now, it makes sense that he might be let go, but I'd also expect he's likely a backup at this point on any team he might go to (given that all teams have Cs already, and we're sitting here just weeks before the draft). You'd think he'd just as soon renegotiate and have a chance to do that in Dallas where he already knows the system and wouldn't have to relocate.