It's not a perfect song obviously, but way better than anything Nickelback has written.
There was a point in time that I quite enjoyed listening to How You Remind Me, and would still consider it a pretty decent pop/rock song. I’m not sure if I ever felt like listening to The Best of Times, even when initially digesting Black Clouds.
You claim to have different criteria for deciding if you like/dislike a song, or if a song is good/bad/better/worse than others (this one clearly revolving more or less entirely around technicality and musicianship). If you need to believe that to justify liking some music that isn’t oh so amazingly written, that’s your business. But as much as you treat your evaluation of a song’s intrinsic quality based on those traits as you tapping into something objective, it is still nothing more than your own personal way of evaluating the question.
Other people are going to approach “what makes a song good or bad?” in a completely different way. There are people to whom technicality in playing means nothing, who are completely indifferent to it, that it’s actually totally different things that matter; or to whom it is a matter of diminishing returns, ie a song should be well played and composed to a certain extent to be good, but there is a point after which technicality does nothing to help a song, and may even hinder it, and the point at which any two people judge that threshold to have been passed could be completely different; or to whom it is important, up to a point, but can’t stand on its own, and can become irrelevant if other things aren’t up to scratch. They might be extremely important factors to you, but that doesn’t make technicality and musicianship objectively divining rods for good music.
You can wax poetic about how great the playing in The Best of Times is in passages and the skill of the guys in DT and so on, but I have never remotely wanted to listen to it. The lyrics are atrocious, and it feels forced and formulaic, like a DT song by numbers, albeit not such a heavy one. How You Remind Me, regardless of its inferior musicianship and simpler ambitions, succeeds in what it tries to achieve; it’s a catchy, listenable rock song that feels genuine. In other words, it’s a far better piece of music. To me.