I don't think he's "played by" Putin, I think Putin has something on him or is benefiting him personally.He/America need to keep up with China and Russia. These countries are far ahead in some areas, eg hypersonic weapons, glide vehicles, space warfare and so on. But these countries can do things much cheaper than the US due to low wages and lower safety standards.
Of course he may just be throwing money at the problem rather than seeing where money can be saved or spent more wisely.
This is all very well if you believe that other countries will keep to the Agreement. But they won't, eg especially the big players like China and Russia and maybe India.
Trump had some decent ideas, but his way of doing things and his own arrogance means he is easily 'played' by other world leaders, eg those of (again) China and Russia.
His recent HBO interview (on Axios) is a clue. The interviewer asked "Okay, even if there is debate about whether or not Russia had bounties on American soldiers, it is well established Russia helped fund the Taliban during our war with Afghanistan, how do you respond?"
And Trump said immediately without waffling a Russian talking point, which was "well, we once helped fund the Taliban against Russia!" Leaving out of course that this was in the 1970s when the US was trying to stop the spread of USSR and authoritarian communism. The interviewer said "but that was a different era!" and looked incredulous and Trump had no real response.
Pretty odd response for an "America first!" guy who says he loves our military.
He has also ridiculed most every world leader except Putin and even when Putin was caught mocking Trump with Assad, Trump said nothing. As thin skinned as he is, he kept silent.
Sure, he says empty things like "no one is tougher on Russia than me!", meanwhile keeping Russia's interest in his foreign policy plans.
It makes no sense unless Putin is paying him, helping him or blackmailing him.