Yes, integer ratios sound better than equal temperament ratios. The downside is that you end up with an instrument that has some integer ratios and some disgust

Yes, integer ratios sound better than equal temperament ratios. The downside is that you end up with an instrument that has some integer ratios and some disgusting wolf intervals because it's mathematically impossible to have all integer ratios between every possible interval in every possible key you might decide to play in. That problem is what equal temperament solves for, and is a good reason to use an electronic tuner unless you know your songs will sound better without.