Basically at higher levels we went from making saves 75-95% of the time to failing saves a similar amount.
3e definitely made a weakness a weakness. Except for the way DR was given out like candy. And then you get the "weapons caddy" to hand out monster-specific gear.
Mechanics drive player behavior.
In 1e spells started out weak then got much more powerful at increasing levels. I.e. a MU-5 does about 50% of a troll's hp of they fail the save against a 3rd level fireball. A MU-10 can outright kill trolls who fail their save against a 3rd level fireball. An MU13 can kill a typical blue dragon (10hd=45hp) with a single fireball if they fail the save.
A 3e Wiz5 does about 25% of a troll's hp of they fail the save against a 3rd level fireball. A wiz10 does 55% vs trolls who fail their save against a 3rd level fireball. The 3e wiz13 fireball(3rd) against an adult blue dragon (21hd=241hp) who didnt save does 15% of its hit points.
A 5E Wiz5 does 33% a trolls hp when they fail the save against the 3rd level fireball. A Wiz10 also does 33% of a trolls hp when they fail the save against a 3rd level fireball, but the save is harder to make. The wiz13 does 12% of the adult blue dragon's 225hp with an unresisted 3rd level fireball.
Essentially, 5e 1st-20th plays like 1e 3rd-13th level.
In 5e they mitigate weak saves by making spells less effective (doubling or tripling hp compared to older editions or giving saves every round), preventing multiple spells with duration via concentration, using concentration interruption to end spells, reducing the number of spell slots available above class level 8 especially for high level (6th-9th) spells, and adding legendary saves.
3e gave everything around double the hp as 1e, lots of DR to bolster saves plus Spell Resistance. Casters could be interrupted, though there was a narrow time window for success.
1e had some flat spell resistance (not as common as 5e legendaries or 3e DR) but mostly used opportunity costs to encourage casters to limit how many spells they cast via time to recover spells. Spell selection was another gating mechanism, and lastly 1e casters spent a lot of effort to avoid losing spells due to easy casting interruption (hiding/taking cover, defensive items & lower level spell slots like blur, mirror image, etc).
So, what were the behaviors? These are all from my experience, YMMV.
1e - MU were prone to "holding action" or throwing darts in common fights that "weren't worth a spell". When possible the would "spin up" before fights, casting buffs, defenses, summons, etc where the duration would get through the fight. The MU basically hid, using magic items (if available) during combat. They would come out to unleash a devastating spell if the danger was high (and they had one prepared). Low level MUs were indistinguishable from thieves, hiding and throwing daggers. Fighters cut through the minor fights and protected the glass cannons so they could get off that dragon-slaying spell.
3e - had plenty of spin up as spells refreshed daily. The offensive blasts were used more often but they were less devastating. Casters still took cover, but that was more hit point management than spell preservation. A caster with the hit points could take the opportunity attacks to move out of combat and then get their spell off. Low level casters were usually crossbow users. Warriors had arrays of DR-defeating weapons (silver shortsword, adamantine axe, cold iron mace, longsword +1...) Warriors got multiple attacks to carve up foes weakened by spells.
5e - casters have reliable cantrips that do warrior-esque damage so they are slinging spells every round. Their damaging spells are impacted but far from devastating. Mostly casters clear out the chaff or would temporarily hinder a BBEG so the warriors could gang up on it. If they have a devastating spell, odds are they can only cast it once a day. "Spinning up" is either potion guzzling or when all the party casters buff one PC (Polymorph:giant ape + enlarge + Armor of Agathys on the warlock was fun) however this means those casters concentrating on spells are hiding.
So...pick your dials to get the play feel you want.