I don't believe questions like this are fair. The most recent 30 years is too recent to make a completely valid judgement... good or bad... on any President. To really know you have to see how their actions and policies shook out. What may have been popular at the time may prove to be a boondoggle, and visa versa.
You are attributing the lesson that bonehead Cheney gleaned from Reagan's Presidency, not anything Reagan himself said and/or may have believed.
That being said... was Cheney wrong? I believe his sentiment was/is repugnant, but let's ask what he meant.
Did he mean "deficits don't matter" as a matter of fiscal policy, and debt should be used to effect policy?
Or, did he mean "deficits don't matter" as a political consideration? That they could run up a deficit and not suffer political fallout for it. Shoot, maybe even gain politically.
Either one is repugnant, but if it is the latter one (political) then he wasn't necessarily wrong... in the sense that in spite of people's whining and moaning over the deficit and debt we still elect and re-elect politicians that are willing to spend us into oblivion. Especially Congress, which is where the real purse strings are anyway.
...and this is why I say we need to see how things shake out. I have long been a Reagan admirer, for the same reasons you state. But, he also greatly increased the drug war and gave us things like civil asset forfeiture which has caused uncountable damage since then. He may have won the Cold war, but replaced it with a war on his own people. Nothing noble about that.