Would be a waste of money to replace that bridge before its useful life was over. Especially since ships headed to the proposed Ingleside container port wouldn't need to pass under it or any other bridge while coming in from the Gulf.
Corpus is at a big disadvantage to Houston when it comes to containers, since Houston is developing into a regional hub of large redistribution facilities, many shipping lines would prefer to offload at one stop rather than a string of ports, by itself is a relatively tiny market, isn't much closer to San Antonio or Mexico, further from Austin and DFW(the largest market), and faces competion for N. Mexican traffic from other Mexican ports. Brownsville may even have a better shot at attracting container traffic than Corpus. The CC port will probably still be dominated by bulk and niche products for a long time into the future.
That's pretty much what I think. There's no need for container facilities in both Corpus Christi and Ingleside. The Harbor Bridge is just 45 years old, and should be easily good till it reaches 100. The promoters of a new bridge say it would have room for shoulders and pedestrian lanes, but that isn' worth spending $100 million+ to replace the existing bridge.