Would a racial feature that lets you learn a low-level spell of your choice be balanced?

Question

Many races give certain low-level spells on a once-per-day basis and there is the high elf who can learn any Wizard cantrip. Now consider the following racial feature:

Choose any first or second level spell. You can cast that spell once without expending a spell slot. If you do, you cannot cast that spell again this way until you finish a long rest. Your spellcasting ability for the spell is Intelligence, Wisdom, or Charisma (your choice).

My question now is if this is problematic, especially from a balance perspective. There are two specific concerns I see that might be relevant:

1. Powerful combat spells, such as Shatter or Guiding Bolt

2. Class specific spells which become available to members of other classes

While there are certainly specific interactions to be exploited here (just like with multiclassing and feat combinations) that is not what I'm interested in. I'm rather interested in general problems posed by certain groups of spells (like the ones named above).

I assume that the once-per-day clause generally prevents abuse. Secondly, many official races already provide such spells, albeit without the choice. Furthermore, this question concluded that making level one spells available once per day via a feat (which some official feats do) poses no problem. That is different from this question, however, in that I am considering a racial feature which can grant spells of levels one and two rather than just level one.

Does this racial feature pose general problems of balance?

I am mostly concerned with overpoweredness which would invalidate otherwise level-appropriate combat encounters and less so with imbalances of damage output between players.

Side note: I am working on a point buy system for racial features, so this will not go into a specific race I'm designing.

Side not 2: I am not sure as of yet how the feature will be valued. Of course, the feature is more valuable than any specific spell, just like the high elf cantrip of choice is more valuable than other features which provide a specific cantrip.

Explanation on the system: My valuation of features is generally based on this analysis found online. I do not make all features available that are found in official races, just a subset which fits the style of my game, but players can freely chose ability score increases (such as +2/+1 to any chosen scores), as well as skill and tool proficiencies and a few other features (such as Dwarven Resilience, Lucky, or a climbing speed).

My current pricing concept works as follows: A once-per-day spell of choice costs 3 points. In total you get an +3 ASI (which can add no more than 2 to a single stat) and 16 points to buy additional options.

Options for 2 points include: an assortment of three tool proficiencies and / or languages; 120 feet darkvision; 35 feet base speed; climbing speed; Trance; Powerful Build; Speak with small beasts.

Other options for 3 points include: an assortment of five tool proficiencies and / or languages; a skill proficiency, a type of armor proficiency; two weapon proficiencies; a cantrip of choice

Options for four points are replacing the +3 ASI with a +4 ASI, or a 40 feet base speed.

Answer 1

The Detect Balance scale is a useful guide to judging a race's power level:

https://www.reddit.com/r/dndnext/comments/53pf0j/detect_balance_an_improved_scale_for_measuring_5e/?utm_source=amp&utm_medium=&utm_content=post_body

On Detect Balance, a pre-selected cantrip is worth 2 points, and choice of cantrip is worth 3. This suggests that the freedom to choose which spell you can cast adds a point to the value of the feature.

You don't state a level that the chosen spell comes online, so it seems that it's available from level 1. Detect Balance states that the ability to cast a 2nd level spell (the more powerful option) once per day at level 1 is 4 points. Extending the principle from cantrips, that would place the choice of a 2nd level spell at 5 points.

The generic scale, meanwhile, states that a "frequently useful" feature is worth 4 points, and an "unusually powerful feature" is worth 8 points. Which means that the above calculation would suggest that choice of a 2nd level spell once per day at 1st level is slightly more powerful than a "frequently useful feature" but less powerful than an "unusually powerful feature".

The strongest feature that the Detect Balance scale lists for an established player race is the variant human choice of feat, which is scored at 20. If you choose to use that feat to gain spellcasting, you could get magic initiate, which gives you two cantrips and a 1st level spell of your choice from a selected class list. Or ritual caster, which gives you two 1st level ritual spells of your choice from a chosen class and the potential to learn any future rituals you come across in written form.

There are also many other feats that give you spells, such as fey-touched, which gives you misty step and one other 1st level spell of your choice; and shadow-touched, which is the same except it grants invisibility instead of misty step. Both of these feats also grant a +1 to an ability score, making them half of an ASI. Note that both invisibility and misty step are 2nd level spells - and powerful ones, too, that are commonly desired by players.

Overall, I think the Detect Balance score of 5 is appropriate for this feature, which means that it's probably not unbalanced.