I wish I had an OED subscription so I could investigate this more carefully, but I absolutely don’t believe that “savory” has always meant umami. It’s true that that if you look at a dictionary like Merriam-Webster today you can find
c : pleasing to the sense of taste or smell especially by reason of effective seasoning
d : having a spicy or salty quality without sweetness
e : being, inducing, or marked by the rich or meaty taste sensation of umami
but this was added recently! Back in 2015 it only had the senses c & d. My guess for how this happened is that this is a back-formation from the Japanese; someone was looking for a less foreign-sounding way to refer to umami, and calqued it as “savory”. (This is a pretty good rendering, because the Japanese word umami うま味 is itself a kind of pun. With a slightly different spelling うまみ it means “tastiness”—i.e. “savory” in sense c.)
I think historically the core meaning has just been c, it was a different word for “tasty”. If you look in Webster 1913, that’s how they define it. (I’m even slightly suspicious of sense d! It certainly occurs in set phrases like “would you like a sweet or savory dish”, but did people really have a coherent concept of non-sweet tastes? But that’s a digression.)
If you search for “savory” in 19th century books on on Google Books, there are a few examples which could plausibly refer to an umami taste, e.g. “a savory stew”, but those are in the minority, equally many hits are for things like “savory herbs”, “a savory fruit”, “savory smell”, which obviously aren’t umami, they are simply things that taste good. And perhaps more importantly, even in the case of meat dishes, the word only seems to be used to mean it tastes good. Obviously I have not done a thorough inventory, but I challenge you to find any historical usages of “savory” as a specific taste, analogous to “sweet” or “salty”.
I’m pretty confident that you will not find any such examples, because the idea of a fifth basic taste did not get generally accepted until the 1980s. E.g. as late as 1999, Alan Davidson writes in The Oxford Companion to Food:
the view that has been most widely accepted, at least in western countries, is that there are four tastes: sweet, bitter, acid (or sour), salt. However, many people believe that one or some of the following should be added to the list: metallic; ‘meaty’ or (to use the Japanese term) umami; astringent; pungent (as in the Chinese list above).
Note that even at this point there apparently was no consensus to translate it as “savory”, since he instead writes “meaty”.
I think this is the basic reason people use the loanword: the idea that umami is a taste a fairly recent scientific discovery and conceptual reorganization, while the word “savory” has been around since Middle English, so if you want a word referring specifically to things that trigger the glutamate/inosinate/guanylate receptor, “savory” would be unworkably ambiguous.
Also, apparently the notion that umami qualifies as a basic taste got accepted thanks to a specific research program by group of Japanese scientists who launched a subfield of umami studies in 1982. It seems pretty dismissive to write it off as orientalism when it was due to the deliberate work of actual people living in the orient!