I use I-880 regularly to get to a vendor in west Alameda (via the tubes); it is quite easy to get to downtown Oakland via the Broadway exit just before the I-980 divergence -- so access from I-880 is not an issue (while it is certainly busy, I've yet to encounter a significant backup on that ramp!). If using one of the several bridges over I-980 is vexing to local residents, that portion of the facility would make an ideal place for "capping"; a park, a farmers' market, a series of bike paths -- there's a multitude of possibilities for usage of the top level of a cap. That would, IMO, be the best -- and most cost-effective -- way of balancing local concerns with systemic efficiency. I-980, as it is situated, constitutes the best way to get from Fremont and the other cities south of Oakland to the east side of Berkeley and, of course, the cities beyond the Caldecott Tunnel.
While a "cap" solution won't likely satisfy groups whose principal purpose is the excising of through routes in urban areas, at least it provides a place where locals can utilize a previously unusable swath of land rather than wait for the long and drawn-out process of deleting an Interstate route to run its course through the bureaucracy and, likely, the court system as well. I'll probably get flack from several quarters for saying this, but -- is the (dubious) enjoyment of dancing on the grave of dead freeways worth the time and effort it takes to accomplish removal -- as well as the major disruption of regional traffic patterns? And just who will be doing such "dancing" -- the purportedly put-upon locals, or the activists who seem to pop up from city to city with the same "solution", always in search of a problem that calls for their attention? In the field of policy analysis, such action is termed the "garbage can" approach to a situation!