It wasn't possible for them to be well managed at the time it mattered. Sears was loaded with debt by private equity ghouls; same story for almost all defunct brick and mortar businesses; Amazon was a factor, but private equity is what actually destroyed them.
Are you suggesting that Jeff Bezos somehow convinced all his PE buddies to tank Sears (and their own loans to it) in order for him to build Amazon with less competition? Because, well, no offense, but that seems like a remarkably naive understanding of capital markets and individual motivations. Especially when it's well documented how Eddie Lampert's libertarian beliefs caused him to run it into the ground.
Thank you for bringing this up. Sears really didn't have a choice, they were a victim of the most pernicious LBO, Gordon Gecko-style strip mining nonsense on the PE spectrum. All private equity is not the same but after seeing two PE deals from the inside (one a leveraged buy out) and another VC one with the "grow at insane place" playbook I think I prefer the naked and aligned greed of the VC model; PE destroyed both of the other companies while the VC one was already doomed.