Please god, become the norm.
I predict nothing will change. Flaws in p-values and confidence intervals have been apparent since almost their inception. Jaynes spoke out against it strongly from the 60's on (see, for example, his 1976 paper "Confidence Intervals vs Bayesian Intervals"). Although I can't find it right now, there was a similar statement about p-values from a medical research association in the late 90's. It's not just a problem of misunderstanding the exact meaning of p-values either. There are deep rooted problems like optional stopping which render it further useless. The problem is that with all its problems, statistical significance provides one major advantage over more meaningful methods: it provides pre-canned tests and a number (.05, .01, etc) that you need to 'beat'. The pre-canned-ness/standardization provides benchmarks for publication.
The good news is they're teaching this in first-year biology classes at my uni. We were specifically instructed in the lab to not write "we accept the null hypothesis" just because p > 0.05. Many students lost marks because they said that on their lab report.