The cap on mining is actually a good example of an inflexible technical solution for a problem that is better solved through flexible governance. There are several problems with it:
Inflation can be a good thing. It can be used to combat deflation, and the absence of inflation can lead to stagnation via the paradox of thrift. There are certain central bank policies that encourage inflation and are known to work pretty well, including QE, which was demonized by a lot of people but has now been proven an effective aid in the recovery from the 2008 crash.
The bitcoin approach focuses on the money supply only, but there are other factors to inflation. There is general agreement among economists that the money supply is the key driver of inflation in the long term, but in the short term, other factors can be involved.
Inflation is possible with a static supply of money, because the amount of money in circulation (versus the amount of money in savings accounts or bonds, or otherwise locked up) can change.
Inflation can also happen even with a static supply of money and no changes in the amount of money in circulation. An example is an oil price shock, caused by an embargo: oil is an input into many manufacturing processes, as well as people's cars, so a general increase in the prices of goods and services can be expected.
So, the bitcoin approach takes away some valuable monetary policy tools and it doesn't actually prevent inflation in the short term. People shouldn't believe that their bitcoins are protected from inflation.
