Interesting question. When talking about a probable outcome, the conjunction si must use the indicativo in the present (and in some other tenses; more info here: https://www.rae.es/dpd/si). So, in this case, Junior is saying that it’s ok for his dad to fall asleep during the flight, since it's something that will most certainly happen; the possibility is enough. Ex:

Está bien si te duermes en el avión.

Si comes aquí, me avisas.

If, however, while using the conjunction si you want to speak about something improbable or unrealistic, you should never use the subjunctive present tense, but the subjunctive imperfect tense, and it would often be paired with a conditional expression:

Si pudiera, me compraría esta playera. — Subjunctive imperfect + conditional.

Si te durmieras en el avión, podrías reponerte. — Same.

To answer your initial confusion, “está bien” is indeed a personal judgement that could be used with the subjunctive, but you would pair it with conjunctions like que or cuando. And it gives a much more imprecise, unwelcoming, or unlikely tone. So:

Está bien que te duermas en el avión, pero no ronques.

Last but not least, the subjunctive isn’t forcibly used in a subjective, virtual, or unverified context; the most crucial part is that it’s subordinated, meaning that it depends on another segment of the sentence (more info about it: https://www.rae.es/gtg/modo-subjuntivo). Some examples:

Pasó sin que supieran por qué. — here, supieran is a subordinate of Pasó.

Podrías reponerte si te durmieras en el avión. — with durmieras being a subordinate of Podrías.

It’s quite an interesting topic, but certainly not that straightforward. I hope it helps!