They are not the same answer because they are not the same situation.
What causes initiative is not 'thinking about attacking' but 'taking hostile action'. The game system then determines whether or not anyone could notice that this 'threat' exists, and may even allow their 'retaliation' to interrupt that 'initial' hostile action, given both noticing the threat and having faster reactions.
Well, you swapped from 'action' to 'threat', so there's that. Secondly, if you don't notice the threat, that's what surprise is for, it's on the tin. You've trying to backdoor in a new surprise mechanic because you don't like how the existing one works.
And that's fine, you can do that, but it's not good play to make your players decide actions with no information.
No, the initiative was not caused by the wizard intending to attack, but by the wizard actually attacking! The rules just allow the possibility that he is noticed as a threat and is beaten to the punch by a faster reacting enemy.
So, we're back to action, good. So the wizard begins his attack, which causes initiative to be rolled. Beginning an attack is noticeable, so everyone knows the wizard is attacking. If they didn't notice the wizard before the attack and/or did not expect the attack, they are surprised. Alert negates surprise, so done. Everyone knows the wizard is attacking, some are surprised, some aren't, either because they had a high enough perception or invested a feat. Don't reduce these limited choices in character build because you wanted to surprise your players, work within the ruleset.
The wizard already said he was attacking. That attempt to attack, successful or not, completed or not, is what triggered the combat. The wizard doesn't get to change his mind about attempting to attack because it was that attempt that started the combat. That attempt has already had a real affect in the world; it already began. The wizard cannot then pretend that he didn't begin the attacking process.
And here's the problem again -- you've decided to change the situation but insist that the players cannot change their decisions that were based on a different set of information. Sure, in this example it's an NPC wizard, but I assume you'd require the same of your players (unless you don't, in which case, huh).
So, a player announces an attack against a foe. Under your assumption, since the player was hidden from the foe, the foe doesn't know that they're there until they act in initiative. The foe cannot be surprised (whichever reason floats your boat) and rolls higher than the player. You pick an action for the foe as if they were not aware of the player, but are aware there is some nebulous threat somewhere. The foe does something that makes the player reconsider their action and they wish to change it, but now, you won't allow this -- they must attack even though you've changed the information they originally based their decision to attack on. Not good.
If, instead, you clearly precipitate initiative, this goes away (as do other corner cases). If they player moving to attack springs from hiding to do so, and this starts initiative, then everyone is aware of the threat, if not everything (like the still hidden rogue ally on the other side of the room that's waiting for the signal). Then you roll initiative and announce surprise. In this case, the player gets a nasty shock because the foe cannot be surprised and gets the jump on them. When it's the rogue's turn, they get to shoot from hiding (or whatever), because you successfully framed the combat with a clear starting event but didn't have to reveal everything (works for players, too). This exact scenario works equally well if you swap the party with the foes.
Yes, but the reason is that there is no encounter at all when the enemy are three miles away! In contrast, the wizard hiding around the corner can be perceived, is taking hostile action, therefore this encounter has already begun.
Firstly, we strongly disagree that there's any way to cast a spell in a clandestine way without subtle spell, so everyone would be aware of the casting starting. Second, if the wizard beginning to cast starts initiative, but no one is aware of it, how is this, in any way, different from the wizard 3 miles away starting initiative by starting to cast teleport? Except for the spell name, it's really not -- no one is aware of the wizard, the wizard can cast with complete stealth, etc., etc. There's no difference in kind, here, perhaps only in scale.
There are no 'gymnastics' and no 'forcing of blind actions'. The PCs do not get to know about the ambushers because they simply have failed to perceive them. That's obvious. That's not twisting anything.
And yet you would force them to take an action without information as to why if they had the temerity to take the Alert feat and roll a higher initiative than your bad guys. So, yes, you do force blind actions on your players.
They are not 'forced' to take their allowed actions, but being able to take actions is better than not being able to take actions. They haven't perceived the enemy yet, so it's their failure to perceive them that is causing them to act 'blindly', not some secret player-screwing DM agenda.
In what way are they not forced to act? It's their initiative, they have to do something, even if it's to do nothing. And, again, the being able to act being better is only true if the enemy will kill them in one hit and they have a chance to avoid that hit through a lucky action. Otherwise, they're in the exact same place they would be by going second -- the enemy's action still happens, doesn't kill or incapacitate them, and now they can meaningfully act.
You're trying to say "sure, I make them act without enough information, but that okay, and good, because they might do something smart by accident." One of the other posters whom you quoted above in solidarity was specifically complaining that a forced blind action could result in their bad guy getting found anyway was unfair (movement uncovers hidden opponent by removing hiding conditions, now allowed to attack seen opponent). You supported this, but seem to allow for it's exact play as a possibility in this angle of your argument. Your position is shaky and you keep changing key points in different defenses that contradict each other. It's not your best argument (and you've made quite a few good arguments I've read in other threads).