If the framers only wanted violations of criminal statutes to be grounds for impeachment

it could have been so defined. It wasn't. If the framers wanted that type of limit placed on the allowable grounds to impeach a president, they easily could have so specified in the constitution. They didn't. Why didn't they? I will venture to say they didn't because there was no consensus that the grounds for impeachment should be so tightly restricted that a President could spend every hour of every day on a golf course for four years and not be subject to impeachment; because no specific statute was broken.

Opinions differed back then on what should be impeachable. They also differed in the 1860's, and in the 1970's, and in the 1990's, but Abuse of Power has always been considered constitutional grounds for impeachment by the House of Representatives.

If the framers were so worried that a partisan congress might move to remove an elected President from office, over an "overly vague" charge such as "Abuse of Power", they could have built in a safeguard to prevent that. Instead of allowing a partisan simple majority to kick a President out of office, they could have raised that bar to require an overwhelming majority to do so, something along the lines of a two thirds vote of Congress... Wait a minute. It turns out that is exactly what they did, and a bar set that high has historically fulfilled it's function. Even Andrew Johnson got to serve out his term of office.

So all of the Republican arguments over eligible grounds for impeachment fail on every count. No President has ever been impeached for abusing his power to proclaim national holidays, or abusing his power to lower flags to half mast, or for abusing his ability to give his friends a ride on Air Force One. The Abuse of Power that Trump is accused of is as serious as a heart attack. The Republican Senate is acting like a hospital emergency room that refuses to examine a patient with severe chest pains because he isn't carrying a prescription for that treatment upon entry.