The restoration of the mitzvah of the decapitated cart in our time

Is it even possible to compare the large number of murders relative to the population of the late Second Temple period (as the Sages describe) to our time?

In any case, let's assume that the annual statistics of unsolved murders will drop to some number close to zero. In such a case, will the mitzvah be restored?

The mitzvah will be restored, but it requires the Great Yard and nearby (and the city to which the measurement is made is also a city that has a yard of 23). See Rambam, Chapter 1, Mahal, Murderer.

The problem is that if murderers are not executed, at least one of the primary reasons for holding the ceremony has been eliminated, the purpose of which is to “make atonement for your people Israel, whom you have redeemed’ and you shall not put innocent blood among your people Israel; and the blood shall be atoned for them” which stands parallel to ”and the land shall not be atoned for the blood that is shed in it, for if by the blood that is shed”

First, as I wrote, there needs to be a close relative here, and this ensures that a sacrifice will be made when there is a ”ed who can kill.
But this is not necessary. The sacrifice can atone for the blood even if the killing of the murderer is no longer practiced. Atonement is not intended only to replace the punishment of the murderer.

A note in the margin of the discussion –
It does not say that they annulled a decapitated calf, but rather “a decapitated calf” was annulled.
This does not mean that the Sanhedrin annulled the law, but rather that the Mishnah may have intended to say that it was God who annulled it. He caused a political situation, the Roman commission that annulled the Great Court, which was a condition for the mitzvah. And it was from God that this was because murderers were numerous. After all, a decapitated calf was meant to resolve rare doubts, and when the situation was that murderers were numerous in the open, God saw no point in continuing with it and turned the situation around so that the mitzvah was actually annulled.

This is also how one can explain “from the multitude of adulterers the bitter waters ceased”. And apparently it is difficult, and since Queen Helen, who lived near the ruins of the temple, prepared a golden tablet for the Parashat Sota, she probably would not have prepared it if she saw that it was no longer working. So when exactly did the bitter waters stop? But God destroyed His temple and thus abolished them.

Interesting.
Rambam 19:2:
Even if the murderer saw a single witness, even a slave or a woman or someone disqualified from testifying in a crime, they would not be beheaded, therefore the murderers openly killed a decapitated calf.
It is clear that this is self-evidently invalid and not that they were annulled. Although it does not seem to be due to political circumstances.