Has he? He's had at least 3 if not 4 clubs outspending him every year and until last season has always finished within the top 4.
The problem hasn't so much been the end result because more often than not they've finished where they 'should', the problem has been that nothing has changed and there's no sign of things changing. Every single issue at Arsenal is exactly the same as 10 years ago.
Supporters want to see progress being made. Even if things ultimately don't quite improve, if there's signs that you're working towards something and are aware of what needs changing then supporters will often be more sympathetic.
Spending more denotes potential for competitiveness, it doesn't correlate to league finishes. A team with a 70mil wage budget isn't going to consistently compete for the league with a bunch of teams spending around 200mil, and a 200mil team won't beat a 190mil team every year but they will consistently (but not every year) beat teams with a 70mil budget.
Arsenal have been around the top 3 in budget and a massive gap from Spurs and those behind for a decade. They should some years compete for first, maybe a couple of years come 5th. Has it been City, Chelsea, Utd, Arsenal every year? Or do those teams change order most years, with some really bad years for both CHelsea and Utd?
We're absolutely in amongst the top wage spenders, we have a huge squad rather than a much smaller higher wage individual squad such as Chelsea or City and there is no reason for it.
Most years when CHelsea/City/Utd went out of the CL, it would be by 1-2 goals against a top team, when Arsenal do it we get blown out of the water by a team and sometimes 'make a come back' in a second leg when the other team has decided not to waste energy after being 4 goals up from the first leg.
4th isn't okay because we spend the 4th highest in the league. 4th highest, and 10 times closer in spending to the top 3 than the 3 below us, means we should be competing in that group, not competing in the group below, nothing more or less. We absolutely should have both won or genuinely competed for(ie, capable of winning in the last 2-3 games of the season still) the league 2-3 times at least in a decade. We shouldn't flop so heavily EVERY year in the champions league and we absolutely shouldn't have the **** poor excuse for a squad we have now.
Leicester, Dortmund, Atletico have all won their leagues while spending 1/3rd of what the biggest team in the league does, 4th highest spender doesn't make finishing 4th okay, at all. Two of those have also been drastically more competitive in the champions league than Arsenal have achieved in the past 10 years. Atletico and Dortmund, still on a fraction of Arsenal's budget, consistently get to latter stages than us.
We have massively underperformed in the past decade. Every team has ups and downs.... except Arsenal has no ups, every single year without fail we flop hard in the massive majority of big games, we fail to show up and that is why we never have an 'up' year.