It is only 'ambiguous' because trying to twist around the wording gives an advantage.
That is what these rules 'questions' come down to.
Trying to find exploits. It is a better game if you just don't.
To be clear, they are having bad wrong fun?
"Exploits" is a loaded word.
Is it an exploit because the effect is stronger?
If someone uses their trident to grapple someone with a hasted action, is that an exploit? Or shoves someone?
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It really is an "ask your DM" situation. And a DM who knee-jerk answers "no" to every such question is one who considers players to be cheaters, which is a pretty crappy way to treat your fellow players.
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In my opinion, I would make it depend on the current state of inter party balance. If the bladesinger is outshining everyone, then no, haste doesn't let you cast a cantrip. If the bladesinger is being clearly outshone, then sure, haste lets you cast a cantrip.
Both are reasonable wordings. In fact, if I found the bladesinger was being outshone badly, I would
suggest that to the bladesinger as a DM.
And the extra few-d8-damage you get from this technique isn't all that huge.
If someone went and made a Hex 2/BS 6/Sorc 3/X 6 EB 12 times and make an attack every round, it would be a special game where someone doing that build was being outshone so much it needs this ruling. (I hereby dub that build Machine Gun Kelly)