In some cases, Chrysler Corp's marketing operatives tried to do some things the general public (mostly a bit ignorant of car brands and such) was just not prepared for.
Basically, Chrysler Corp had a line/brand of vehicles which equated to similar General Motors line/brands. Plymouth was Chevy (entry level), then Dodge was Pontiac, DeSoto was Oldsmobile, Chrysler was Buick, and Imperial was Cadillac . . . in that order of hierarchy. Nothing was wrong with that, especially after GM declared that "What was good for GM was good for the country".
In some respects, Ford was more efficient in their marketing, having fewer resources. Ford tried to cover everything with Ford, with Lincoln getting Cadillac. Then adding Mercury in the late 1930s to catch the middle stuff.
When Lincoln brought out their new (first time sold) Continental in 1955, branded as "not a Lincoln", but sold only by Lincoln dealers, the Chrysler operatives probably said "WE can do that, too!", so the separate Imperial brand was born . . . "not a Chrysler", at the top of the model mountain. Looking at the original "Imperial" cars, it was not hard to see their lineage and blood lines in the 1955 Chryslers, but when the new 1957 chassis/platform cars hit, then the Imperial was more about something other than just a longer wheelbase. Looking at the print ads, they were about prestige and elegance, with a new Imperial logo to go with that.
Chrysler had been building in-house limos under the guise of "8-passenger DeSoto sedans", mostly used as taxis in larger cities (as New York), even seen in some exterior shots in the tv series "Amos and Andy", just that those shots were lower resolution so the front of the car was not seen. Then Cadillac started to build similar cars for a few years starting in 1959!!! Except the Cadillacs were aimed at the corporate executives and such, who wanted to take their assistants with them, or body guards.
Although there were many print ads in the major consumer magazines of the later 1950s, "LIFE" and "LOOK", etc., to many people who might have seen then, they were "just another car ad", for something they couldn't afford in the tight economy of those times. Basically, ignored by people not interested in such things.
Considering "eliteness", the lower-production Imperials certainly got that point, if it mattered. Everybody who had money still drove Cadillacs with some opting for Lincolns, but still very few opting for Imperials. Although the famous Tom McCahill of "Popular Mechanics" magazine very plainly admitting to owning Imperials as "The Best Road Car in America" (paraphrasing), when being a great car for cross-country trips really mattered, in a time before the expansive Interstate Highway system was started to have been built. Cornering, a firmer suspension for bumpy roads, and "passing gear power" were safety features which Cadillacs and Lincolns did not have to the same degree as normal Chryslers AND Imperials had due to their engineering blood lines.
Now, IF you want to see some eye-opening comparisons, look at the several segments of "On The Test Track with the 1957 Chrysler Products" on YouTube. No Imperials in those vids, but the Chrysler-brand cars are compared to their GM counterparts. Then there are a few more comparing the Chryslers to Mercurys. The great roadability of the torsion bar/leaf spring Chryslers is so far above what the competition had it is unreal!!!!!
THEN, that one segment where the cars encounter a rural railroad crossing and then a sudden elevation change (lower), where the integrity of the Chrysler UniBody structure is graphically demonstrated as the cars hit that sudden lower elevation angle. So much for that quieter and smoother-riding GM body/frame configuration if it can't keep the bumper from moving so much in relation to the rest of the car body.
Back in the early 1960s, I had a favorite uncle (who knew about cars and what made them "tick"), he lived down near Houston, TX (with smoother roads). He normal drove Oldsmobiles and Buicks. When he would come to visit and also go out to see older relatives "on the dirt roads" of the rural areas, one day he was out wiping down the door weatherstrips on his '60 LeSabre 4-dr sedan with a silicone-lube'd rag. I asked him what he was doing and he said that those dirt roads and dust made the weaterhstrips squeak, so this lube stopped that and kept them quiet. As I knew that I had never seen my Father do that on our '56 Plymouth and the weatherstrips did not squeak. But I later determined that GM's body/frame cars were more prone to this than Fords or Chrysler products.
Through all of the "Chrysler Products are BETTER" ads of those 1950-1960 eras, few people seemed to notice and Chrysler remained #3 in corporate sales after GM and Ford. Few conquest sales for Chrysler brands, whereas consumers might switch between GM and Ford brands a bit, by observation. Only people who really understood or appreciated the Chrysler way of doing things seemed to keep buying them, by observation. Not to forget that many of the Chrysler dealers tended to be a bit flakier to deal with than similar GM or Ford dealers. Chryslers got bad-mouthed for things that GM dealers got "a big PASS" on, it seemed. Even back then, it seemed that Chrysler tried to design things "too good", but to do otherwise would have put them in the same "mediocre, with a few exceptions" category that Ford (and especially) GM was in.
Sorry for the length. Just some thoughts and long-time observations,