Well, how about this:
ls . -r -file -fi *.html | cp -d /home/new_dir/
It is a bit shorter than your bash equivalent, still doing the same thing.
I think you're mistaken about what `cp` (`Copy-Item`) is intended to do. Its main purpose is to copy, not to filter. Yes, `Copy-Item` supports filtering because it's part of the "common parameters", but to be more in line with the cmdlets' original purposes, you should `ls` (`Get-ChildItem`) first, because it has more filtering capability, and then pipe the results to `cp`.
Is it complex? No, actually its complexity is exactly the same as that of your `find` example! `find` is more or less equivalent to `ls` in that both gathers the list of files that meet certain criteria. And then, like `find` invokes `cp` multiple times to do actual copying, `ls` (`Get-ChildItem`) feeds its result to `cp` (`Copy-Item`). They are structured in a similar way.
I'd even say the PS one-liner is more akin to "the UNIX philosophy". In the bash one-liner, there is a direct parent-child relationship between `find` and `cp`, which doesn't utilize pipes at all. Whereas the PS one-liner connects two equivalent processes (`ls` and `cp`) with a pipe. This is exactly what I'd call "small processes work together to get the job done", which is again the UNIX way.