The new School of Invention tradition for Wizards (Unearthed Arcana) while still in playtesting (and indeed a bit silly in my opinion, more of a "chaos wizard"), got me thinking about its reckless casting ability. This allows the caster to cast magic they do not have prepared and get a random result. The random spells have different targeting criteria (Wall of Stone, Fireball, Feign Death , Mass Cure Wounds) and so it is not possible to decide the target of the spell until it has been cast, as you don't know what you are going to get until it is cast.
This suggests that the designer of the subclass has made the assumption that you don't actually target until you have cast the spell and release it, which makes sense from one point of view, strongly supported by the way a prepared action casting works, PHB p.193 where you cast the spell and hold the energy until the condition is met for the readied action at which point you target the spell.
While the Unearthed Arcana is not RAW or finalized and released, my question is not about this subclass, but about the official rules as a whole.
Is there was any direct RAW, or other supporting or opposing RAW, that states at what point a caster defines the target of a spell?
As a sub-question: are there any circumstances where it actually matters, other than the already defined Readied Action spell casting, in the official rules?
Best Answer
No explicit RAW, but evidence suggests target is selected when spell is released
General Rule
As you mention in your question, the part of the text dealing with readying the spell is the most compelling piece of evidence the book has:
Combined with the Sage Advice, Rules Answers: June 2016:
Together, these pieces create a compelling case for a general rule.
While readying a spell (per the SA ruling) you can specify the target of the spell when the spell is released not when the spell is cast (related). And, because the description says that you "cast [the spell] as normal" there is solid evidence that that is the normal behavior of spells in general.
Thus, the general rule we glean from this is: a spell's target is determined when the spell is released but after it is cast.
What about spells with longer casting times?
They follow the same ruling above because they are not considered to be cast until you have completed the casting process for the requisite amount of time:
So there is really no difference between these spells and spells of any other casting time. At the end of the specified casting time, the spell is cast. When it is then released, targets must be selected for the spell.
When does it matter? Never (or extremely rarely)
Edge cases not covered by current rules are few if not non-existent as far as I can tell right now.
The only time this distinction matters is when there is a difference in time between the casting and the releasing (or the effects) of the spell. The only current cases of that are readying an action to cast a spell and specific spells (eg Glyph of Warding(Spell Glyph)) that specify the rules within the spell description.
The fact that spellcasting has worked seemingly perfectly well despite the lack of an explicit ruling in this case lends further support to the fact that such a general rule is probably not necessary (outside of what has already been explicitly said). It doesn't seem like there are an abundance or even any edge cases that aren't covered under the current rules.
It doesn't matter for the UA School of Invention Wizard
I know you did not need or want an answer focused on the UA part of your question. However, it is worth noting that even the UA Invention Wizard that inspired the question would not fall into the category of a case in which this distinction actually matters. Per the current description of reckless casting:
Both options have the player roll and then have the wizard cast the spell that results. The only difference to normal casting is the random roll. There is no separation in time between the casting and the effect of the spell that would make targeting unclear.