Yeah, “there is no asset inflation” doesn't seem to actually be a common belief.
“Asset inflation is different in kind than consumer price inflation and not what normal people discussing inflation care about” is more common.
I'm not sure why monetarily-driven asset inflation would be an issue at all, unless one expected the driving monetary force to not merely be removed (returning to a more typical long-term pattern of asset price changes), but undone (such that the current overall lift above the prior long-term trend would be unwound before returning to the prior long-term slope.) Producing a monetarily-driven transient bubble.
It's not implausible that that could occur under some circumstances, but I'm not aware of any evidence that there would be anyway of distinguishing circumstances that might indicate it. Certainly, there's no obvious reason to assume such a monetary bubble is the normal case with monetarily-driven asset inflation.
Its been one of the main causes in inequality and unaffordable house prices so is very important. It also makes the economy vulnerable to big drops in prices which could/will happen.
I think most people agree there is a lot of asset inflation. Your link doesn't match your quote either.