I think Phoenix and Elixir is actually an excellent platforom to built e-commerce/marketplace platforms from scratch. This is different question from if you should build e-commerce platforms from scratch at all.
If you do make the decision that you build it from scratch, however, either a dedicated software for your business, hosted solution for many businesses or something you’d license to others - in my humble opinion it’s good choice to build it with Elixir and Phoenix.
Being able to scale up, being able to handle abusive clients (web crawlers/scrapers used heavily in the industry), being able to monitor things, perform long-running operations such as reporting, reaching out to external services (payemnt gateways etc) en masse etc. BEAM/Erlang/Elixir eliminates tones of problems that are being faced by the industry when they desing similar systems say in Ruby. Shopify would do well switching from Ruby to Elixir, for example (again, in my opinion). I’d say they’d definitely cut down on the hosting cost and simplify infrastructure significantly.
I don’t think Elixir is good choice if you want to use something out of the box, in most cases, as the libraries are simply not there. But if you’ve already made the decision you need to build custom stuff, go ahead and use it.