Sears had one big problem when Eddie took over: it was out of step with the then-current retail format (big box stores). Its stores were heavily situated in enclosed malls that were out of fashion. The solution was straightforward if expensive: reformat the business (Sears had already done this twice before).
But then Eddie rolled into town with his genius consultants and a galaxy brained idea: Kmart has stand-alone stores that kinda look like big box if you squint. So let's just merge the brands together! Then Sears ends up in big boxes without expensive reformatting!
The fact that the brands were completely incompatible was pointed out by everyone who knew anything, but those weren't people in Eddie's inner circle so their opinions meant nothing.
By the way I don't think ESL Investments ended up making money on Sears. They stripped the company of assets yes, but most of those assets were distressed by the collapse of Sears. Like a lot of real estate was in struggling malls that had Sears as the anchor tenant. ISTR some of ESL's LPs suing Eddie.
Eddie made money the way all PE fund managers make money even when everyone else involved loses their shirt: by charging fees.
