I want to create subtasks without creating projects because projects cause me to lose sight of tasks.
Unfortunately, it's not possible on Todoist to have tasks that don't belong into any project. If you don't have a need to sort tasks by their goal/theme etc. you can of course add them all to the default "Inbox" project. Please note that you can always view tasks from all your projects on the date-based views (if they have dates) and when searching for "viewall" (this will show all tasks even those without dates).
To create a sub-task, simply enter the Inbox project, click on "Add task" and the bottom on the list and with the task input field opened, either click on the arrow icons on the right side of this field or use the keyboard shortcuts Ctrl+RightArrow and Ctrl+LeftArrow to indent/unindent a task.
But you can create sub tasks on the mobile app. Why is that?
Any task or sub-task you create will be added into a project. On our mobile app, it will suggest you the default "Inbox" project.