Possibly it would, but criminal investigation is imperfect by default and can't just be compared to an ideal of justice done exactly right and swiftly. Instead it has to manage with the reality of its difficulty and a killer being imprisoned decades later, the families of his victims being able to confront him vs. never having known anything at all.

You can make whatever excuses you want about any individual case, but this discussion is about clearance rates, and it’s obviously preferable for a larger proportion of homicide cases to be cleared within a reasonable time span.

The moment you mandate fast clearance you get into a state where people game the system, which can have bad side effects in criminal justice. You would likely find that either the wrong person is charged more frequently or else cases are rubber stamped closed to keep number up.

Murder clearance rate in Czechia is between 93 and 100 per cent depending on the year, but it is likely easier to solve murders in a relatively small language community. Although we are part of the Schengen free movement area, which means that at least some murderers will try to escape.