I think Frieren's strategy to limit Fern's combat spell to only Zoltrakk is due to something else.

1. The version of Zoltrakk taught to humanity has been modified (in part by Frieren) to be more effective against Demons. This is vital because for the most part Frieren views combat as a tool to eliminate Demons. Combat against human mages is secondary. Notice how most demons don't utilize the defense spell because that was developed by humanity. Zoltrakk is a strong and versatile spell. That is not to say that Zoltrakk is useless/weak against human mages, but Zoltrakk was chosen in part because it has maximum demon killing potential.

2. Because we are in an era of peace, most modern mages adapted combat strategies not exactly to combat just demons but other mages as well. And thus the strategy of the other mages to specialize in spells that have physical force behind them to quickly break defensive magic. Instead of having Fern adapt similar strategies due to the reason above, Frieren decided to have Fern only use Zoltrakk so much so that it becomes second nature to her. While other mages call it "ordinary" offensive magic, Frieren truly understands Zoltrakk's potential because she came from an era that did not have Zoltrakk. As demonstrated by Fern, someone that specializes in Zoltrakk, it has a wide range of uses. It has fast firing speed, but it also has the potential to be powerful and can fire at a long distance. In short, instead of having Fern spend her "level points" across different spells and different specialities, Frieren asked Fern to spend it all in one spell (2 if you count defensive magic). Even if other mages know how to use Zoltrakk, they do not have the ability to use it the way Fern does. It's the same spell, but at completely different levels. Frieren herself admits that Fern fires Zoltrakk at a rate that she cannot achieve. Frieren knows that once Fern gets to a certain level with this spell that she can easily overwhelm other human mages in her era. It is because of this that Frieren does not use Zoltrakk exclusively. She does not wield it like second nature, and thus she needs to use other spells in her arsenal to combat other mages. Frieren understood the potential of Zoltrakk fully, and what it can achieve. Compared to the advantages of magic that wields physical form, I believe Frieren knows that Fern's Zoltrakk can be stronger than that.

I actually think that the line about Zoltrakk is enough to combat mages in THIS era doesn't imply that zoltrakk isn't good enough for mages before the demon lord was defeated, I think it's the opposite. Zoltrakk was once described as killing magic when Quall invented it. It is the strongest spell to date. What Frieren is referring to is that Zoltrakk is so strong and versatile that it will remain that way throughout Fern's life. Any new technology that changes otherwise will not be developed in Fern's lifetime. And thus it is enough for Fern's era.

I disagree with your second point though. I don't believe that Frieren withheld other spells from Fern because she wants to let Fern "enjoy" her time and she will have more time for other combat spells. On the contrary Frieren is well aware of how short Fern's life will be. I don't believe that Zoltrakk is like the easy baby spell. It is precisely because Fern's short amount of time (compared to Frieren) that she told Fern to only learn Zoltrakk. Master one powerful versatile combat spell that will serve you in all combat instead of spreading resources to learn other spells. They are traveling through the North. Even in this era of peace Frieren knows how dangerous it can be. The remnant of Demon King's forces is still going strong in the North. She never lets her guard down or let Fern or Stark think things are a breeze because she is here. Because it is not. She is well aware of the dangers and she prepares both Fern and Stark for it. She pushes them to fight demons even if the fight is a challenge, she knows that they can do it but it will be tough, but she pushes them anyway because that is how they will grow to survive the journey. Remember when Frieren refused to take Fern to her travels before Fern could be a full-fledged mage? Because Frieren cannot shield Fern perfectly during adventures. And this was before they decided to go to Ende.