Why?
“Why?”
Probably a lot of reasons. One may be that even Putin wants clicks. Others may be, Putin wants to be seen as a leader. There is no risk in making this suggestion and it may cause discussion that could potentially be uncomfortable for Trump. (Incidentally, I think Trump’s skin is thicker than elephant hide.) There is a long running stalemate which is costing Russia more than it can afford and Putin would like to calm things down. Also, and most importantly, Trump is prone to grand gestures and could possibly accept. This could be the start of an agreement that ends the conflict. And, lastly, it costs nothing to make the offer and could, potentially, add a positive dimension to the conflict.
When Trump met with the North Korean leader, it changed the dynamic of the “conflict” there. I think we haven’t seen the end of that beginning yet. Either Kim will lose power or he will bend to Trump’s will and NK will slowly enter the rest of the world. (No matter what, I don’t think Kim will last as long as his father did. Things have changed too much for that.)