That's the standard casting time for a cantrip. Some are bonus actions and at least one is longer than 1 action, but those are specific beats general versions of cantrips. The ability does not specifically quicken cantrips, so it has no ability to take a 1 minute casting and reduce it to part of an action.
Okay, so you're picking 1 action as the "standard casting time of cantrips". That sounds like very general of a rule. So isn't the rule of being able to cast a cantrip as an attack during an attack action - a very specific rule - take precedent over it?
No. This is a False Dichotomy.
Disagree. You have a non-rule that you generalized from looking at casting times for cantrips. I only use the rules. It is not a false dichotomy that a cantrip is a cantrip, not only cantrips with a specific casting time. This arguement does not hold up.
In addition to not specifying that it makes an exception for longer casting times than normal,
Which it doesn't have to, since there's no actual rule about cantrip casting times. It's like asking to list an exception for heavy weapons that they can be used in an Attack action. There literally is nothing in the rules to seperate them out, so there is no need for an exception. You noticing a pattern that most cantrips have the same casting time does not mean that is a rule.
Please, unless you can quote a rule about cantrip having a casting time, please make your arguments assuming it is NOT a rule and therefore holds no weight. It is a pattern, but that pattern holds no rule weight so no rule exceptions need to be listed.
We can also look at existing rules to see if the are exception. There are magic items that cast spells, and they use the Activate an Item action (DMG 141). It is an action. Now, if casts a spell that is a bonus action to cast, it's still using the Activate an Item action, which is a full action. There's no exception that needs to be listed that magic items can have spells that take different amounts of time to cast normally. It's just a spell, with no implication that a magic item can only cast spells that take 1 action. It's the same thing.
it also specifies that it's part of the attack, so you need to be attacking with the cantrip. The attack action specifies that you are making an attack on a target, so a spell cast using the Bladesinger ability as part of that attack must also attack the target. Mending fails on that front as well.
This is a very different argument, and one I'd be much more inclined to agree with you on.
Then the next time I want to cast lightning bolt as a bonus action I'll be sure to tell the DM that nothing is different about 1 action vs. 1 minute vs. bonus action. Since nothing is different, 1 action = 1 bonus action and I can do that, right?
Lightning bolt has a rule that says it's one action to cast. So it's one action to cast. I never said they were the same in the general, I said the Bladesinger ability does not differentiate.
An attack takes 1 action of time. The ability allows you to sub a cantrip in for your extra attack as part of that 1 action. Anything longer than 1 action cannot by definition take 1 action to do unless something specifically changes the casting time such as the Sorcerer's Quicken Spell ability. Since 1 minute is in fact much different from 1 action, it can't be used as part of a single action without a very explicit exception.
We know for a fact this is not true. Going back to magic items, the Staff of the Magi specifically allows you to take an action to cast a number of spells, which includes Conjure Elemental which takes a minute to cast. It doesn't change the casting time, it just lets you do it with an action.