Point casters can have a variable number of top level and first level spell options in a day. If they put all their points in top level ones they can do more than a standard 5e caster, but then are out of lower-level spell options. If they chose to cast first level spells instead of free cantrips, they can do this a lot more than 5e standard casters, but at the cost of their higher-level spells in that day.
I don't think that's really the biggest problem with point buy magic, or even how in practice point buy magic works.
The problem with point buy is simple - it's simply much harder to design and much harder to balance than some sort of slot-based system with fixed effects and consequently requires orders of magnitude more playtesting to get right. This is true if we are talking about point buy chargen or point buy magic systems.
A typical point buy system is no more balanced than the typical prices on an equipment list. Numbers are pulled out of the air and chosen for reasons of elegance and the resulting system is about as well balanced as a Magic the Gathering card list. And how the players will ultimately respond to the system is fundamentally the same. Overtime they'll gravitate to "decks" of effects that are the most potent and under-costed.
Yes, this happens in spell-slot systems too but in point buy the situation is more acute and more pronounced. Initial divergence will be met with dissatisfaction as players realize that some other player's build with the same points is vastly more powerful and more useful in vastly more situations.
Regardless of where in your chargen point buy happens, whether across the board or just in the magic system, there will be strong convergence on those builds that are the most useful, leading to a number of rather standardized builds that effectively become the classes of the game, much like the Standard MtG environment rather quickly converges to not the infinite number of decks possible but just those that are close enough in power to be somewhat effective. Invariably, in an RPG these will be some variation of Johnny One-Shot who invests heavily in that one thing so that they are a hammer in a world full of nails. They will not be as you might imagine without experience nuanced versions of characters who are broadly skilled, as however realistic such builds might be these leads to jacks of all trades and masters of none that fail at everything. And it will turn out that underneath this desire for customization, the real inspirations of the players tend to be solo heroic protagonists in narrative fiction who are de facto if not outright de jure masters of all trades and the underlying desire was to make "Batman" or "James Bond" or "Sherlock Holmes" or "Indiana Jones" or "Riddick" or "Rand Al'Thor" or "Aragorn" or whatever.
In short, point buy based systems while they may have their place don't ultimately in practice do much of anything a class-based system does. Even with something like CoC in the BRP system, you'll very soon discover that as an outcome you end up with classes. And if you have something as ambitious as GURPs what you'll very soon discover is that as an outcome you only end up with a mess.
Any functional magic point buy system must stop players from "Going Nova". Going Nova is the main problem with any magic system in that players are always tempted to spend all their resources at once. This problem becomes more acute in point buy and if the rules allow for it, it really has no good solution. This means any good point buy system has some pretty hard caps on how much points you can invest into a spell to upcast it, as upcasting is almost always better than not upcasting for the same reason Johnny One Shot is able to pound every nail but Jack of all Trades can pound none. But if you strongly limit upcasting, then you are starting to approach a slot-based system anyway, particularly one that is quasi-Vancian like the 3e Sorcerer. Yes, point buy is a bit more flexible than that, but the tradeoffs are so huge in mental space of both design and play, that it's not at all clear to me that it's worth it.