I recall having the same reaction when I first starting fiddling with Savage Worlds. At the end of the day, its not an issue but one does have to keep a few things in mind. But lets get the first implied question out of the way.
But what about a PC wizard? He'd have to be legendary just to have half the spells the lich does. Some of the spells are pretty flexible, but others are rather narrow.
Point blank, the game does not end when one reaches Legendary. Some might even say life begins at Legendary

. Especially for the classic fantasy campaign, running 200xp and 300xp characters are not out of the question. Our group has one campaign we set in Ptolus (SW mixes guns and magic much smoother than D&D anyway) that ended the first story arc at 100xp. I am running 50 Fathoms right now, but we plan to go back to Ptolus and run those PCs for another 100xp story arc. We may do that multiple times just do see what the system can do.
So when you put it in that perspective, that all ties together very nicely.
To your actual question
My question: Is there some sort of variant rule for this in a Savage Worlds expansion? They can't just let you learn 5 spells with each additional edge (for instance) and keep the system balanced. But if they don't do something, you really can't play a versatile wizard--you're stuck with characters with very focused powers.
Big picture, Savage Worlds "wizards" tend to play like D&D 3.x sorcerers. I do agree there is a dearth of "I have a spell for that" spells. Lots of little utility spells like Knock are missing at least directly (which I will throw out some ideas for separately). But D&D has a lot of non-scaling spells that as one levels requires one to get the Improved version, whether it is named as such or not. Lets fact it, a 10th level Wizard in D&D is going to have a lot of useless spells in their spellbook. Magic Missile might still have a use, but Charm Person is very weak without using a Metamagic Feat (which is akin to taking a higher powered variant). Spells like Cure Light Wounds and Monster Summoning I become less utilized except by very clever players. In Savage Worlds, Healing and Summon "scale" automatically. Most area effect damage spells are just variants of Burst and Blast - you have to pick them up every few levels just to keep up.
So D&D has a lot of spells because the system requires it based on the scaling of the system. In the end, many a wizard and sorcerers wind up using the same 5 or 6 spells all the time and Savage Worlds does the same thing. It just does not keep changing names every couple of levels.
But what about all those utility spells? Some are quite frankly not in the system and not easily replicated (Mount for example). But even the aforemented Knock is there in a variation - Boost Trait - cast it on the Lockpick guy to ensure you get the door open. Sure its not the auto unlock of Knock - but quite frankly Knock is a bad spell for a number of reasons. Namely, it steals the thunder of what another class is doing. Boost/Lower trait (and its cousin that is area effect) is great way to simulate the helpful/general weaking spells across D&D.
Clever use of trappings replacates spells from D&D in creative ways (although I tend to avoid what I call D&D trappings anyway - I have played D&D for a long time - its time to mix up of the flavor). A clever application of Entangle can be used for Tasha's Hideous Laughter - just have the trapping change it to Spirit instead of Agility to break free. Entangle can be used for all sorts of "crowd control" spells, not just the obvious Web/Entangle.
So to me, D&D has a smaller number of spells when you categorized them by what they do and realize all the description or minor system variations are Trappings.
But lets answer your real question - "How do I make Wizards feel more 'Wizard-y'?"
First off, most Savage Worlds spells have a "second spell" built right into them when you get a Raise on the casting. By getting the raise, you trigger the Improved Version. This really becomes noticeable at Legendary when you pile on the Professional Edge. Rolling d12+2/d6+2 guarantees the spell works and gives you very good odds of getting a Raise (so extra damage, extra effect, etc). It subtle, but I really noticed it when we went back to the those aforementioned 110xp Ptolus characters - characters generally got raises when doing the things they are very good at. So give the Raise version of your spell a name too! Now spending a Bennie to get the Raise gives rise to "ah, he is trying for Maylocks Death Grip instead of Torak's Horrid Embrace".
A big key getting more "magical" is to apply magic trappings to Everything and describe it as such when using things other than Powers. For example, your Wizard infuses his body with magic to permanently harden his skin that also slows poisons in his system - that is simply bumping Vigor up a die (lets face it, its not like the wizard is starting a workout regiment - it must be magic that is causing his increase in hardiness). I ran a psionist in that aforementioned game. Here are three psionic trappings I used to describe non-spell advancements:
https://rogues-gallery.obsidianportal.com/items/pensieve-armor
https://rogues-gallery.obsidianportal.com/adventure-log/parallel-processing
https://rogues-gallery.obsidianportal.com/posts/kinetic-absorption
The armor one is for a magic item, but could easily have been applied to a skill advance. Skills are just low powered spells that are just activated a different way. My psionist "cast his mind out to search out thoughts and feelings" when he did his Streetwise roll. Stealth was a weak level Invisibility spell. Notice was more him sensing other thoughts and minds nearby that might be a danger than "seeing or hearing".
Can you do this in D&D? Sure, but 3.x made it hard to do given all the Keywords. It was easier just to make a new spell or Feat than to try to reskin an existing one.
Does it work? Well, one player in the group said because I used the trappings for everything he could never tell if what I was doing was due to a skill, an Edge, or a Power. I am very proud of the comment.