I'm curious about why the entire screen is filled with inputs. Is it because the job is complicated, and the user should be highly skilled and trained?

The user is, or will quickly be, very familiar with the forms. The forms have been the same for decades, some users have even been using them that long. They occasionally need to jump around the form to reference other data so tabs and wizards slow them down.

Also, the forms are filled out differently based on customer defined rules which vary widely and change frequently, especially around qualitative questions. For large, long-term projects, the final form is hidden, qualitative questions are turned into multiple quantitative questions and mapped to the final answer so the user doesn't have to constantly think about the custom rules. But for small projects, it's too much development work and the user is expected to follow the rules manually.

Rapid data entry and Web app/site/page cannot be put in the same sentence.

From experience I agree, but is it impossible or are the current frameworks just lacking?

Usually some terminal UI is the best for rapid data entry, which is why a shop I used to work at switched back to their TUI because the shiny new GUI was blocking everything.

The TUI you had to learn and the GUI was intuitive, but after a week anybody could use the TUI at the same speed and after a month they'd 10x or and soon 100x the entry speed.