Many monetary rules call for higher rates of price inflation if the economy starts to enter a downturn. That's often the right economic prescription, but voters hate high inflation.
Tyler is engaged in "reasoning from a price change". A term like 'inflation' doesn't mean much of anything to the public, and certainly not what economists like Tyler mean by the term. When I used to poll my students, I'd find that 99% of students conflated 'inflation' with supply-side inflation. I'd ask, "Suppose all wages and prices rose by exactly 10%, has the cost of living actually increased?" I'd guess 99% would get the answer wrong. (Yes, the cost of living has increased, but they'd say no.)
When the public expresses a concern about inflation, what they really are referring to is living standards. Thus when there is supply-side inflation, prices rise faster than incomes, and living standards fall. That's the type of inflation the public has in mind when they express opposition to inflation. In contrast, when there is demand-side inflation the public sees their income rise faster than prices, so living standards rise (in the short run.)
If the public really did oppose demand-side inflation then they should have greatly enjoyed the economy of 2009. After all, a fall in AD brought inflation down to zero. And yet living standards plunged, because the demand-side disinflation caused incomes to fall faster than inflation. If the Fed had a more inflationary policy during 2009 then the public would have been much happier, as there would not have been as big a decline in real income. A much milder recession and less severe asset price collapse.
Did voters prefer the economy of 2006 or 2009?
Again, never reason from a price change. How people feel about a price change depends entirely on whether it's caused by an aggregate supply shift or a demand shift.
In addition, don't take seriously the answers you get from polls of public opinion. When you ask the public how they feel about inflation, they are (in their own minds) holding their own nominal income constant and visualizing rising prices. No surprise that that isn't popular! Thus their answer doesn't really tell you what they think about inflation, and certainly not what they think about demand-side inflation created by the Fed. Rather their answer tells you what they think about supply-side inflation. Yes, we all hate adverse supply shocks. But beyond that the public has no opinion, as they don't really even understand what inflation is.
PS. Also, don't confuse incomes with hourly wages. An unexpected demand-side inflation lowers real hourly wages while raising real incomes and real asset prices. People care far more about their overall real incomes and real asset prices than they do about their real hourly wages.
PPS. The first time I ever recall a politician running on an explicit platform of higher inflation was in 2012. Abe won a massive victory on a promise of higher inflation, in a country where a huge share of voters are old people on fixed incomes. He ended deflation in Japan and was re-elected overwhelmingly. (We'll see how he does this time.)