Aaaah...no!
Not just "no", "h*ll no!"
Putin is first and foremost a KGB thug, and if you forget that for a second, it's to your mortal danger.
Putin is second of all, one of if not the richest man in Russia, so Putin is an olagarch!
Third, Putin is a Russian expansionist/imperialist, who wishes most to restore the old Soviet Empire.
So the only real wars Putin is fighting are the ones he started.
Fourth, Putin is a dictator which means he has nothing in common with traditional American conservatism.
Your claim above that "Lincoln, Wilson, Roosevelt, Nixon, Bush and Obama all did things similar to Putin" is absurd by any objective measure.
Certainly, Putin is not Stalin, but he is a dictator from a mold vastly different than any US president, wartime or not.
Does that mean the US cannot get along with Putin?
No, of course not -- in 1941 when faced with a common enemy more deadly than any today, the US & Brits teamed up successfully with Stalin, a dictator more brutal than any today.
And that, I believe, is all President Trump is talking about when he says, "wouldn't it be nice?".
But teaming-up is one thing, general political admiration for dictators is something only the Left does, never American conservatives.
Putin is the Czar. A modern version and embodies all the characteristics - Autocrat of all the Russias of past Czars.
This obviously does not make him a democrat. Continued use of Cold War expressions misstate what he is. The Czars of past history were absolutist & oligarchs. If they wanted to be the richest man in Russia they could do so with the wave of their hand. Primarily he is a Russian nationalist. Too many Americans associate the word Czar with Nicholas II. Probably the only Czar they have heard of or know anything about. Nicholas II was J. Wellington Wimpy compared to his predecessors.
None of what I have said should be interpreted as liking or preference for Putin. Its just a recognition that Russia has returned to the past (Its roots!) in the type of leadership it wants.
That being said there is no reason for viewing Russia with automatic hostility. Through most of our history relations with Russia were not close but respectful. I see no reason why we can’t return to that.