He did it just to make Trump look weak and mission accomplished.So why would Putin go through this charade just to tell Trump to go pound sand? He could have done that without leaving Moscow.
He only stayed an hour and could had just as easily done it over the phone like you said. I voted for Trump all 3 times, but Putin and Zelensky are their respective nations' leaders in a real war and Trump is just a salesman in a sense. They both can spot BS when they see it.
You could tell by Trump's body language he's truly frustrated with both of them and doesn't really know what to do next, either. There would be nothing wrong in walking away from both sides in the short term and just let them duke it out. Put it on the Euro countries and see what happens.