2. They hired David Moyes
Ok. Your original claim was that it will be easy for the next manager to compete, the point is that it's also easy for there to be a slip when a long time and successful manager leaves, regardless of how good a team is set up.
When you add to that the fact that the old manager is basically the entire club (as Ferguson was at United) it makes it even harder for another manager to come in and step in.
Arsenal *could* hire the next great manager. They could also hire the next David Moyes.
3. They didn't give him any time.
Sure they didn't give him time, but maybe he's also just not a very good manager. It was United's first time finishing outside of the top 3 since 1991. It's understandable that people didn't think Moyes was the solution.
4. Then the season after they finished in a champions league spot.
Yes, in 14-15 they barely made it back to a CL spot, while also having disappointing seasons in the FA cup and the league cup. Then the next year they bombed out of the CL at the group stage and barely held onto 5th.
Just because Arsenal finishes out of a CL place doesn't mean they will be stuck in midtable hell.
There's a big difference between not competing for a title/not always in CL spots and midtable hell. I wouldn't say either United or Liverpool were in midtable hell, but apart from the miracle season 3 years ago, neither have competed for a title and neither have been remotely considered locks for the top 4 the last few years.
I'm not expecting Arsenal to suddenly become Stoke where they finish between 9th and 13th every single year, but there's plenty of room between Stoke and what Arsenal are right now.
1. United had an aging core.
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And look at the age of Ramsay, Wilshere, Xhaka, Bellerin, Ox, Iwobi, etc. if you're talking about young up and coming team.
Ages: 26, 24, 24, 22, 23, 20
Now let's look at United in Ferguson's last season.
Rooney, Nani, Kagawa, Chicharito, Jones, deGea, Welbeck, Smalling.
Ages: 26, 25, 23, 24, 20, 21, 21, 22. They also had van Persie, Vidic, and Evra just like Arsenal has Sanchez, Ozil and Giroud
The core of Arsenal you listed is neither young nor elite.
A young core would be like Spurs have. Kane, Alli, Son, and Dier, all 24 or under. If you expand it to 25 you add Eriksen, Lamela, and Wanyama. Rose and Walker are 26 (soon 27)