This a challenging question!
Lets start with first principles. Inflation is traditionally measured by the Consumer Price Index (CPI). While there are other measure, it is the measure most quoted. Critically, it's composition has three major components:
- Services (e.g. labor)
- Food & Energy (Commodities)
Over the long-run, commodity prices tend to decline in real terms with oil the lone materiel exception. This obivates the need to watch commodities. Thus, most inflation watchers look at core inflation, which covers housing and services.
Increasing in the prices of housing or services are the two critical elements for higher inflation. How do we get those higher prices?
Monetarist argue that an expansionary money supply will increase the the price level and thus give rise to inflation. Critical to this outcome is that either wages or credit expands, so that more money is in circulation to bid up prices. Thus, even if the Federal Reserve expands the money supply banks must be willing to lend and companies must be willing to raise wages for it to have an impact. This was important during te Financial Crisis because banks were not lending and wages were not increasing. Thus, monetary expansion had little effect.
Certainly, the 'disintermediation' of labor has occurred with technology, lower union power, and outsourcing. While the number of people employed in manufacturing and mining have declined, the production has increased. This a technology impact. Lower union participation rates have reduced teh ability of laobor to negotiate higher prices. Thus wages pressure is lower.
Further, technology and lower transportation costs have enabled the outsourcing of many former manufacturing and call service jobs. Effectively, technology enabled a billion English speaking people from Inida to join the global labor force while China's entry into the WTO in 2001 enabled then to add a billion people for manufacturing. This is a huge supply of labor. The problem is the freeflow of capital and products is not matched by free labor. Low cost labor (e.g., China) is able to replace high cost labor (e.g. US).
So, a higher supply of labor and a lower demand as technology progresses conspires to keep the price of labor down, and thus mute inflation.
Housing has enjoyed strong growth, the financial crisis notwithstanding. This is due to limited housing supply, low interest rates, and higher credit availability. Further, foreign buyers can dominate some local real estate markets (e.g. Vancouver, CAN and Syndney, AU) . Even though prices have increased in some markets (e.g. tech hubs like SF and Seattle), low demand in other US markets have kept the national rate in check.
Further, housing inflation is measured by "Owner's Equivalent Rent" that accounts for 2/3 of the housing component. Each month, they ask homeowners how much they would rent their house for, which is interesting becasue of the inherent bias: people will not say that they will rent for less than their cost, which sresulted in no change in the housing inflation during the financial crisis even as prices dropped 25%!
Critically, the large US trading deficit ensures that China and OPEC countries buy US Treasuries and thus limiting the impact of monetary policy. As you highlight, the lower interst rates serve to increase financial asset prices while not materially impacting the real economy, so you see financial asset inflation, which has little economic value.
In summary, inflation has any causes, and how it is measured is important. Further, the ability of monetary policy to drive outcomes is muted due to secular changes in the global economy. Combined with the disflationary pressure from the producitivity enhancement form the Millennial generation makes the inflation of difficult event to achieve.
A final note: think about the current situation: a near doubling of Oil prices in the last year, the tightest job market in 50 years, and interest rates still near generational lows, but inflation is under the Fed target of 2%. Inflation should be high by standard economic models, So either our measures are less than ideal (maybe) or global productivity and the global labor supply is keeping a lid on domestic inflation.