That video may have failed to make you understand the benefits of the let it crash philosophy in the BEAM, The BEAM was developed by Ericson with this let it crash mantra at is core for running a telephony system that could never go down. So, no web requests, just backend stuff 
Please bear in mind that just watching talks can lead you to a misunderstanding of what a language good fit is, because sometimes it may lack the full context to you due to your lack of knowledge with the language. I recommend you to also read some books or do some video courses from reputable sources.
So, I strongly recommend you to first read this book or make this video by @pragdave as I recommend here:
After doing it you will have a better understanding about the let it crash philosophy and how it can help you isolate errors on your system in order to keep it running without downtime.
Be aware that the BEAM and Elixir doesn’t do miracles and solve developer bad decisions in terms of architecture.
As a a previous PHP developer that had used also cron jobs or queues to keep the system working and in sync I can tell you that Elixir is an excellent fit for your use case.
