DM when you look at teams budgets you don't just look at what they spend on transfer fees in 1 year. It's the complete package, the total cost of their squad, the amount they're spending on wages and of course their net spend year on year.
By budgets I'm not simply talking about transfer fees spent that 1 year. There is of course the wage bill and you can't ignore the total cost of teams' squads too. City might not spend a penny next summer and have a negative net spend but they're still going to have a £400m+ squad available to them.
Wenger has had less resources to available to him (cost of his squad, money to spend to improve his squad and wage bill) than at least 3 other sides over the last 10 years or so. Obviously you want him to do more with what he has available but I'm not sure how you can expect him to do so.
You seem to have missed the point as well, that means that on average Arsenal shouldn't be as competitive as often, it doesn't mean they can't win the league nor compete in some years.
Wage bill wise, Arsenal have been pretty damn close to UTd till very recently and that is more about buying more players more recently having 'newer' wages.
arsenal have huge resources, on top of that people like to completely forget that Wenger has a monumental advantage over every other manager in the league, and actually europe, longevity. If Guardiola bought a kid who thought would be the next big thing for 4mil.... that would now be potentially a 50mil player for Bayern... not City. If Wenger did the same that player would still be at Arsenal. Wenger doesn't have to spend as much because he at no stage in the past decade has had to replace a squad in the space of 3 years, or panic buy(he has, but he's had the resources, time and backing in place to prevent it). Wenger turned down the chance to buy Mbappe a year ago because the agents wanted 8million. No other manager has had the ability to plan for the future, to buy cheaper, to shape players from younger and cheaper. The problem is Wenger is buying absolute stinkers, Ox and Walcott for pretty damn big money at 16 before they'd done anything and most importantly both players look no better than the day they signed, they aren't more complete players, they don't play any differently.
Guardiola literally stated that they spent big this summer because the club hadn't planned for the future and had no fullbacks, but had he been around for 10 years he would have been training and buying younger cheaper players and making the players they have better.
Old Wenger, up to 2005, improved almost every player in the team, we bought a 5mil player and they were sold at 30mil, when was the last time we truly did this, when was the last time market value didn't just increase the player cost. Poch has improved the value of the squad he had several times over by training the players he had to be better players. There is a hell of a lot of value to be had from both time, wise spending and most importantly, excellent coaching. I can't remember the last player Arsenal had who actually improved massively after Arsenal bought them, yet there is literally a dozen or more from just the past two years at Spurs. Walker and Rose were fairly deemed to be awful full backs, two years under Poch and Walker goes for 50mil.
City, Chelsea and Utd could have spent 1/3rd of what they have done, jesus the players Chelsea have bought since 03/04 and simply thrown away barely being used, for half the value because they wanted them off the books, it's laughable. Wenger again because of longevity hasn't been buying 40mil midfielders to throw them away 1-2 years later, hasn't spent 20mil for a bench warmer who plays 3 games before being shoved out the door at a 15mil loss.
Up until a couple of years ago Utd were only spending 10-15mil more on wages than Arsenal and up until Fergie left, they weren't spending crazily on transfers either despite having success. Notice how much value Fergie got by being a long term manager. The difference between Fergi and Wenger post 2004, is Fergie kept buying players, improving them and having squads that improved, a winning mentality and not bottling every single season when there was a bit of pressure on.
Utd have been spending considerably more, considerably quicker.... and doing much worse than under Fergie, does that fit with your "money is everything" mantra, UTd spent less on transfers and wages than Chelsea and City by some massive margin.... but kept winning more titles than both.
Again I've not said they should even win a single title, but they absolutely, 100% certainly should have been more competitive and in more actual title fights. We led the league 2 seasons ago as City, Chelsea, Utd, all screwed up..... what did I say... we'll still bottle it because that is what this squad does every single year without fail. That is what we did. Also again Spurs may have only finished ahead of them for one season officially, but 2 years ago Spurs were in the title fight, well, lets see.
https://www.premierleague.com/tables?co=1&se=42&mw=1-20&ha=-1
match week 20, Arsenal 42 points, Leicester 40, City 39, Spurs 36.
Match week 30, Leic 63, Spurs 58, Arsenal 52, from 2 point lead to 11 points behind in 10 games, pitiful.
Week 34, Spurs still only 5 points back, Arsenal 10 points back with only 12 points to play for.
Week 35, Spurs 7 points back, Arsenal 12, 9 points to play for, Arsenal out of the title race despite how poor City, Chelsea and Utd had been.
Arsenal had the lead and despite a manager with ~20 years at Arsenal, huge experience, a much higher wage bill, higher transfer spending... we bottled it from Jan through to early May. Spurs fought back from 6 points down at week 20 to losing out on the title with a draw to a top team(Chelsea) before after the league was over, performing extremely poorly in 2 games that meant absolutely nothing at all. But a young side without much experience in their first title fight... being crap after the fight is over is significantly better than bottling it while in the lead without any excuses at all.