Removing "all traces" of Safari could mean removing Webkit and its supporting libraries.
(and, yes, the next OS update would simply reinstall those standard Apple apps.)
Webkit is used by a fairly wide range of OTHER apps, and would disable such apps as Mail, Google Chrome, some other Apple apps that provide access to your internet connection, perhaps breaking some of the OTHER software that you used, or at least giving you unintended results.
You can do quite a bit to ignore Safari by changing the setting for "Default web browser" in System Preferences/General tab.
I am fed up with Safari, not a good browser it has been nothing but trouble. Also not happy that the latest version doesn't work with DuckDuckGo. I am already ignoring it - and have made Firefox my default. I would have liked to be completely rid of Safari but if it isn't a practical idea I may well forget it.
Not sure what might be happening on your system.
I am running latest Safari ver 12.1 on Mojave 10.14.1, and DuckDuckGo works with no problem. In fact, I have had DDGo set as my default search engine in Safari for several years, and it never fails for me.
Maybe you have an outdated extension installed in Safari that does not work correctly. Safari DOES struggle with some ad blockers that have not been updated yet (or in some case, won't ever be updated.)
But, if you have other struggles, then there remain a lot of alternate browsers that you can use: Google Chrome, Opera, OmniWeb, Roccat browser, iCab, Firefox developer version. Those, plus a couple others, are what I have on my system, and each gets used regularly for specific purposes. Most used for me, however, is Safari.
OK, so DDG works, but not that setting? Is that your only complaint about Safari?
hmm... Safari's built-in website tracking settings (in the Privacy tab) are sufficient for me.
Otherwise, I still prefer DuckDuckGo's simplicity .
I believe that Safari is good Webkit browser! However like all browser just make sure you go to the program's Preference's and not have the browser auto-open downloaded programs, only open downloaded programs manually! This is a simple thing to stop Trojans that are compressed!
Now have you deleted your history, cookies and cache yet? download the simple program YASU] and run all the cleaning programs and have the free program reboot your Mac, I bet this will help your Safari problems!
The only thing I dislike is the resource hog of Chrome for Mac because it is a resource hog on all Mac OS versions, so go with something different for a second browser!