Is it possible to develop Lightning Web Components without using SFDX? I'm wondering if we can develop LWC using Illuminated Cloud (IntelliJ) or VS Code IDEs. I saw LWC create options in Illuminated Cloud, but not sure how it would work? Any reference would be also great.
In Short: yes that is possible LWC does not depend on SFDX Some Clarification:
SFDX stands for Salesforce Developer Experience .
The Salesforce Developer Experience (DX) is a set of tools that streamlines the entire development life cycle. It improves team development and collaboration, facilitates automated testing and continuous integration, and makes the release cycle more efficient and agile.
It has nothing (directly) to do with what is available on Platform or not
The SFDX Cli is a command line wrapping some tools which provides many plugins used by SFDX in order to provide Tooling around Development, Testing and Code Synchronization but in the end it can also be used completly out of DX Context in order e. g. to write other useful Administrator / Development Automation Tasks
Illuminated Cloud and other bigger IDEs (like Welkin Suite have support for it. Or you can manually deploy them via Metadata Api (e. g. via Ant or Workbench. LWC is represtented by the LightningComponentBundle Metadata => See Metadata Api. For Development with VS Code you need the Salesforce Extension Pack which in returns requires the installed CLI - but as explained above -> if you want to develop in the "old" model without any scratch orgs etc. it will be absolutely no problem. The Extensions support "Development on any org" since end of last year
As per documentation there are other IDE as well for developing Lightning Web Component like Illuminated Cloud but VS Code has beautiful integration with Salesforce CLI. So it as always preferred to use VS Code for Lightning Web Component Development.