It doesn't work properly. "have become any better" would work. I would probably change "it" to "this".
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TakaIf the sentence was affirmative, as something like this, then would it work?The economy has started to recover, and this may imply that our living standards have become all the better.I would say this is acceptable without being an obvious use of "all the better".
TakaWhat do you mean by "without being an obvious use"?"Even though it's not a typical way of using that expression", or something?Yes, it is not the most typical way of using that expression.