Chicago recognized some flaws and got a new coach and built around Toews, Kane, Keith and Seabrook (all draft picks)
LA Recognized some flaws and got a new coach and built around Doughty, Brown and Kopitar (all draft picks)
Pittsburgh recognized some flaws and got a new coach and built around Crosby, Malkin and Fleury (all draft picks)
Boston traded Thornton, gave up on the goalies and got a new coach......
There is something to be said about coaching change based on the talent that is there, build around the core and create a system with the players who are the main.
You build around Hall, Nurse, RNH get the right coach and move forward.
You make a valid point here. The issue though is - and it goes back to what I was saying earlier - the Oilers young core is very soft and not foundation material as it stands today.
Let's compare your examples...
Chicago - Toews, Kane, Keith and Seabrook. Kane is the only one here that is purely a skilled, finesse player. Toews is one of the best 200 foot game players on the planet. Keith is full of aggressiveness and spunk. Seabrook is a monster. All 4 of these guys have been through the wars and are physically and mentally tough enough to win multiple Cups.
Los Angeles - Kopitar, Brown, Doughty, Quick. Again, you're looking at tons of heart and character there. And Brown is (was) one of the premier heart-and-soul captains in the league who hit everything in sight for years. None of these guys are soft... at all.
Pittsburgh - Crosby, Malkin, Letang (Staal at the time), Fleury. Not only are Crosby and Malkin two of the most elite offensive weapons in the NHL, they are both far from soft. They get into scrums and never back down from anything. They are horses that carry teams on their backs. Letang is no softie either.
If I were running the Oilers, I would identify my main foundation as Hall, Eberle, Draisaitl and Nurse. Despite the trade rumors, Eberle is one of the last players on the team I'd trade. RNH is also a potential core piece, but I'd be willing to trade him in the "right" deal if push came to shove. But it would take a major blockbuster to do so.
Yakupov, Schultz and Perron are pieces that I would actively shop for players who are better fits and fill pressing needs. Yakupov and Schultz are the two I would shop the most because they both have sexy names and could fetch a good return IMO.
If the Oilers could parlay Yakupov and Schultz into better, 2-way players with more grit and tenacity (even if they're not as talented) it would be a big win for Edmonton long-term.
After making those two trades, you give the new guys a few months then re-access the make-up of the team in the summer.