Firstly, I'm super biased as I'm the CEO of a product analytics company where one of the value props is getting the data in real time. I agree with this post that people will look at single data points out of context and weight the evidence much more strongly than they should be. Analytics should be one of many tools you use that informs your understanding of how customers are using your product. I also agree that I see a lot of early stage startups invest way too much in building out real-time analytics stores without thinking about what they value they get out of it. That's not something you should do until you're in the 100+ engineer range.
That said, this is a post-hoc justification of why having real-time analytics is bad. Delaying the data by 24 hours doesn't automatically make significance testing better or force people to incorporate more context when interpreting their data. If that's the issue, fix that problem, don't blame the tools.
There's a ton of positive value to having real time data. Just off the top of my head:
1) If you've instrumented something incorrectly you can see that and fix it right away
2) Even worse, if you've accidentally messed up a feature with a release you can know about it right away. This happened to one of our customers recently and without a real-time analytics system they wouldn't have caught it quickly (and this is a tech startup that's well regarded for their engineering that everyone here would know the name of).
3) You can observe significant changes to your user base right away, eg during a launch or if you're getting a lot of new users from a specific channel.
4) It allows you to have more confidence in deploying multiple times a day. It's a little crazy to me that the deployment of a product is faster than our ability to measure it.
I think the real issue is that we're in the early days of analytics and people don't have a great understanding of how to leverage their tools properly. It's like web search before Google or file sync before Dropbox. People will look at single data points and conclude totally crazy things. They won't have an understanding of basic things like the amount of fluctuation on a week to week basis. The largest analytics provider in the world (Google) gives away their product as an ancillary service to drive you to purchase more ads, not to have a better understanding of how your customers are using your product. I'm hopeful this will change over the next 5 years though (and for us to be a part of that!)