Why do all/majority of loan contracts charge nominal interest rate instead of fixed real interest rate?

There are practical problems with having 'real loan' even though theoretically they would actually be desirable (as paper "The Impact of Inflation on Long-Term Housing Loans" by Tschach, Ingo E.) if they would be practical.

1. We do not know what the current inflation is.

This statement is simply incorrect:

Of course we will need to know the current inflation rate, but it's not like this information is secret, so it shouldn't be a problem.

When you look at inflation statistics they do not report actual inflation, they report the estimation of what the inflation is. The inflation estimation is based on a basket of goods that is considered representative and most statistical offices try their best to appropriately capture inflation but it is still just the best estimate and it is generally agreed that all inflation measures have some non-trivial flaws. They for example often do not appropriately capture changes in quality of goods due to technology and it is also highly questionable how different items should be weighted. Those two issues are just an examples there are many more, you can have a look at this investopedia article that explores the main issues in measuring inflation (but not all).

This issue could be circumvented by bank and client agreeing that some inflation measure such as CPI would be considered the inflation but that would cause some serious trouble down the road. For example, what if statistical office decides to update its CPI measure in a way to benefit borrowers or vice versa? The way we measure inflation evolves over time and thus using some real loan based on an ever evolving measure instead of actual inflation would not eliminate inflation related risk completely.

2. Inflation is rarely reported in real time.

Even the best statistical offices usually have about 3-1 month lag in measuring inflation and the most recent measurements of inflation can relatively often be revised later.

This creates another problem as it would make it very difficult to determine each month what the inflation is and hence what actually should be the interest rate paid. All loans would have to be paid with a lag that could even differ per country and due to the possibility of revisions banks would have to send out refunds or send out requests for customers to pay more as the revisions occur.

In future it might be possible to track inflation in real time. There is for example the billion prices project that attempts to do so. However, measuring inflation in real time is still in its infancy and the projects also has its own additional problem of being biased toward goods that are sold by e-commerce and it does not solve the problems in 1.

3. Even though you are correct in saying:

Borrowers and lenders would know that neither of them would benefit from inflation/deflation at cost of the other side, so borrowers would be more willing to borrow and lenders would be more willing to lend

this is basically what the authors of the paper linked above show in their simulations. You are not correct in stating that this would make the loan more predictable. It eliminates the inflation risk of the loan but as Giskard points out you are paid in nominal terms not real terms so the real value you need to transfer back to the bank is not more predictable per se.