Gimp’s way is not really a standard or widely loved, it does get some negative feedback as well.
Generally in Krita it’s recommended to use File -> Export for non-.kra formats. That way Krita will recognize that the file hasn’t been saved yet.
I would like to have a better solution for that though, for example what you say, an option to constrain Save to .kra files. However I know there are other people who disagrees that this kind of saving is dangerous and just blame it all on user error. Which is true - but for example I am nearly always using Save Incremental Version (which doesn’t ask the user anything, just create a new filename and save), so when I, not so long ago, opened a .jpg file and started to make changes, and then used Save Incremental Version a few times and closed Krita, later I realized that it was all filename.jpg, filename_001.jpg, filename_002.jpg. Useless. And there was no “checkbox” to check that I want the .kra file as well (which is present if you use Save for the first time), so there was no time I had to make a conscious decision whether I want .jpg or .kra.
This means it basically needs a solution that won’t be annoying for naysayers.
Oh btw - “If the reason Krita behaves this way is to appeal to Photoshop users” - nope, it’s never the reason, in this case it’s because that’s what people expects. There was also a thread on that already: Option to get a warning message if saving to non-.kra file and here: Save function to show the .kra option by default