Just because no one will arrest Putin doesn't mean nothing will happen. On the contrary, it's a big problem for Russia.
First of all, it's a big symbolic step to isolate Russia even further from the free and democratic world. If some people still had illusions the west will tire of this war at some point (and Russia's only hope is betting on exactly this) and relations will get slowly better again like after 2014 because we need their cheap energy, this arrest warrant says otherwise. You can't have good relations with a wanted war criminal, no matter how much time passes. That further isolation will also tank their economy even harder.
Secondly, from now on he needs an assurance of immunity every time he wants to travel abroad. For somebody who thinks he's a tsar, this is a humiliation to ask and confirm every country he plans to visit to give him immunity.
His humiliation is also a humiliation of the russian narrative of the mighty russian empire that the west fear. Putin's arrest warrant showed them, that we see him just as a common criminal and won't forgive any of his war crimes in the past, present or future. Their propagandists will ridicule it of course, but in reality they should be fuming that their leader is on the same level now as bin Laden or Milosevic for example.
And last but not least, his elite and propagandists understand now that even if Putin himself get's an arrest warrant, none of them is save from international justice and they don't have Putins protection and immunity.
And there are probably even way more consequences.