A draft document containing some scientific use-cases of <5 minute alerts currently lives in this private lsst-dmsst repository: https://github.com/lsst-dmsst/alert-latency
To summarize: at the time of writing that document, it seems that most alerts-related science goals would be satisfied with a 5 minute alert timescale, but that the quickly evolving fields of fast radio bursts and gravitational wave events – and time domain astronomy more broadly – may soon provide more robust motivation for a 60 second latency.
Since there is currently no tabled proposal to change OTT1, there is no reason to improve this draft to the level of a real DMTN. If that changes in the future, a new ticket can be made to resume this investigation (and possibly add more technical aspects to the cost/benefit of longer latencies, if needed).
Noting here, for future reference: #tvs slack discussion Tue Jul 2, suggestion that low-latency alerts from ToO observations important because "jet-powered (http://arxiv.org/abs/1705.10797) and/or proto-magnetar-powered (http://arxiv.org/abs/1508.07939) UV (and X-ray) transients from binary neutron star mergers are predicted to be detectable only up to ~1000 s following the merger." Om Sharan Salafia
But Eric Bellm points out that it's not yet clear "whether the 60 second latency could be achieved for rapid TOO observations in any case: in the standard survey we expect to have to do a fair amount of pre-caching of slow database queries to get alerts out in time, which is possible because the next pointings are known ahead of time. Potentially for a rapid TOO there wouldn’t be time for those to be executed before the images are taken, which would impose some further delay."