Yes, I entirely agree, pilots should experience as many types as they are able, and they should appreciate the fine, and far superior handling of some types. Don't just settle for Cessna/Piper handling, as being the be all and end all of flying, there's more to it than that. But the "more to it" is on many different fronts of how a plane flies, and what it can do, also don't fixate on demanding one element of perfection, if you feel that a broader appreciation of flying is what you want.
If a steadfast Chipmunk pilot flew my Teal, they would be mortally offended by its ridiculous roll handling in the air, until they touched the water where they wanted to be that day. They would come to realize that the poor handling in the air was a compromise to assure it would do what it must on the water. (Huge chord, unbalance ailerons are terrible in the air, but vital in lifting a wingtip float out of the water at very low speed). The guy who designed it knew this, and once explained it to me when I complained about the plane. That sloppy handling plane took me, and all of my gear, to a magnificent coastal camping site in Labrador and back, 260 miles from any town, airport, or fuel - and that was the job of the day.
Strive for the "best", but also accept what you must (albeit airworthy), to get the flying job you need to do - done. If you stand on the ground waiting for the perfect plane to taxi up to you, you're not going to fly anywhere near as much as those of us who will smile, and accept appalling handling.