For 'by the same token' you apply some kind of rule: eg. I give praise when I see an effort being made; by the same token, I am likely to be critical if I come across laziness or sloppy work. The rule is here that I will draw attention to something.
In your example we can't say a rule is being used. I could say as it turned out, we didn't need any.
It is not the tense that is a problem, it is the lack of relationship of the two activities. Note the meaning of the idiom: 'for the same reasons'. What is the 'same reason' that 'he hasn't come up with any ideas' and 'we haven't needed any'? It is not evident in the sentence, so the idiom does not make sense.
Thank you for the comments. I understood the sentence so that "there weren't any new ideas put forward, neither did we need any". But I may be wrong. Thank you anyway.