That's because you're used to them, that's fine. Many of those actions can be done via key combos or other keys (esp on a Mac), like C+R to refresh, C+Sh+I for browser console or Enter to rename a file. Function keys at this point are certainly old school and could even be considered an atavism, like the Print Screen button or the numeric keypad.
Some functions have replacements, others don't. Just one example: both F5 and CTRL-R in browsers do a refresh; CTRL-F5 does a hard refresh (also renews the cache); I don't think there's a non-function-key alternative for that. Losing the function keys would be a major nuisance.
The numeric keypad is useful to me too. A bit less than the function keys, perhaps, but when entering a list of numbers it works so much better. What's more: keyboards without numeric keypad also tend not to have the section with ins/del, home/end, pgup/pgdn and arrow keys; instead those keys are often arranged in cumbersome and inconsistent layouts. I use those a lot too.
I don't know in exactly which meaning you use the word "atavism", but I do know that having all these keys available, in a familiar layout, is very very useful to me.
In the meaning of outdated artifacts, like those turbo buttons on old PC boxes or three button mice. Fn + arrow keys or fn+bksp for del easily replace the specific navigation keys and are for me easier to find by touch with less movement of the wrist.
I had the impression you meant something like that, but I wasn't sure (I'm not a native English speaker) so I looked it up and the dictionary gave me a different meaning, so that got me confused.
Tons of software uses the function keys, especially Windows/cross-platform software. Lots of engineering tools, editing tools, content authoring, programming, etc.
Removing them would break compatibility with an awful lot of things, including Windows itself (which lots of people run using Bootcamp or Parallels). Maybe they're weird, I don't know. Momentum is a powerful force, especially when it comes to software design.
Also for the record, Print Screen takes a screenshot on Windows (and on a lot of Linux systems), which is intuitive and simple. Just because you don't use it doesn't mean it's an abandoned key.
