I think you got a few things mixed up here!
Nope.
IDE's not wanting to include anything else than .h files doesn't mean code should be in .h files. If you want to use code from a.c in b.c you should link a.o and b.o into a_and_b_linked.bin and not try to include a.c into b.c. I know some programmers do the latter but it is very bad coding practise.
For libraries like this one it's much easier to copy a .h file over and #include it in the main file than it is to copy two files over and start messing around with the linker. This is especially true when you need to work on multiple platforms and would need to mess around with the linker multiple times.
Leave the "separate interface and implementation" for big, long-term development, not little projects where you just want to pull a few libraries together as fast as possible. I'll take a big #include ".h" file over "download 50 files along with an out-of-date makefile and try to turn then into a working .lib file" any day of the week.
Hmm.. well, if the act of copying files is the main bottleneck in your project, you may have a point. But as soon as you have to
use these files, it will quickly become a problem. For one, as I already mentioned before, your embedded project will quickly need an MCU with a bigger flash size as the implicit inlining can copy your functions wherever they are called from. Also, in case you need to include these files from multiple locations, you may alternatively run into multiple definition linker errors depending on if said .h file has any definitions outside of the class body.
Basically, giving up good coding practices for the sake of 'easy copying' is a really bad idea. What if your project evolves into something bigger: you want to then split up and rewrite all those .h files and add .cpp files? Maybe for hacking some throw-away stuff together it could be ok, but that's about it.
And your main statement about
"In 2017 we prefer all the code in the .h file and no .cpp file at all." is just plain wrong, sorry. If you change 'we' to 'I', then it's fine of course