Structural monitoring with sensors is indeed possible. The issues are the cost of monitoring, and which parts can actually be monitored.
The more critical a bridge is, the more likely it is to be worth paying the cost of monitoring (criticalness being mainly due to number of vehicles crossing per day, but also the availability of alternate routes and the length of it (i.e. number of vehicles which may be on it during collapse) play a part). A major bridge built these days is likely to have some sort of monitoring built into it, as noted in the article you linked, and an example of which is the Forth Replacement Crossing (now called the Queensferry Crossing). Some bridges have had systems retrofitted, such as the existing Forth Road Bridge, which has acoustic monitoring to listen for cables snapping.
Existing bridges are most likely to be fitted with monitoring if an assessment shows that there is cause for concern. If a bridge assessment finds that part of the bridge is deteriorating, it may recommend more frequent inspections, or the installation of monitoring. Because of the cost of monitoring, this is likely to only happen on major bridges.
So, could monitoring have prevented the I35-W collapse?
Firstly: I35-W, although not a small bridge, was not on the same scale as the Golden Gate Bridge or the Forth bridges. Monitoring was hence only likely to be installed if the bridge had been identified as deficient. And that hadn't happened because the routine bridge inspections and assessments had failed to notice that a small connecting plate was undersized. Your link to sensors seems to suggest that new cheaper sensors may now be available. I still can't see the cost as being affordable given the shear number of bridges which each authority has control over, but maybe over a long period (say 50 years as the budget might stretch to 2% of an authority's bridges per year - numbers plucked completely out of the air by me) it could happen.
Secondly: I don't believe most monitoring is realtime. 87
Although I'm sure monitoring systems have automatic alarms that go off if significant movement occurs, I struggle to believe that someone would have a particularly fast response to it. More than likely, a system alarm would result in someone going to have a look, maybe the same day maybe not. Mainly the systems are there to look at long term issues. Taking the Forth Road Bridge as an example - the acoustic monitoring is there to record the "ping" from a cable strand snapping. There are a few thousand individual strands making up the suspension cables. The acoustic monitoring is there so that someone can look at the results and say "it looks like 63 have snapped in the past six months, maybe we should think about doing something to reduce the load". I don't think it's really there with the expectation that it will record 100 snapping in a day, resulting in the bridge being instantaneously closed. (The Forth Road Bridge closes due to high wind a few times a year - they have a proper system in place to close it).
Thirdly: the official report into the collapse suggests that the failure was very sudden: there was maybe 10 seconds warning. Even with realtime monitoring, you need to a) receive results, b) determine that they're catastrophically bad (easy if you have the 100 pings in my Forth example, difficult if you have accelerometers as per your link, which might be telling you that the bridge moved 0.05 degrees) and c) get the police out there to close the bridge. Total time estimation: 10minutes if you're very lucky. Not 10 seconds. (And probably more like 3 months if you set up the monitoring for long term effects and weren't sure whether the 0.05 degrees was significant or not, because the system wasn't set up for that.)
Disclaimer - I've tried to put in facts and references where I can, but the actual conclusions I've come to are heavily based on my opinions and are not straight facts. 87