http://www.transferleague.co.uk/premiership-transfers/arsenal-transfers.html
In the last 3 years,
Arse, net spend: £53.8M + £32.5M + £8.6M= £94.9
Chls net spend: £16.1M + £49.3M + £72M = £137.4
Chelsea have spent bigger than Arsenal, as have Man Utd and Man City.
Arsenal, are 4th in the spending league.
So 4th in the table is status quo.
So, in reality, if you replace Wenger, you should do so only if Mourinho is willing join Arsenal. I doubt any other manager in the World would be able to get into 3rd. And to win the league - Mourinho will need a huge amount of luck.
Based on the above, Wenger is doing a decent job. Not great, but decent.
Net spend means absolutely god damned nothing at all. If you have £80million and buy 2 crap £40million players you've still spent £80million badly, just because you sell a £40mil player doesn't mean you haven't spent £80million.
In recent seasons we've spent £82mil, £42.5mil, £52mil, £53mil and bought almost no one we should have.
But again you're comparing a short term manager with a long term one. Arsenal could have bought 10 youngsters for 200k a piece who could/should be part of the first team now, Mourinho couldn't because he wasn't there 10 years ago(well he almost was actually but this time around it's not like decisions he made that long ago are effecting the team he has now).
Wenger has a monumental advantage that no other manager in any of the top leagues has, longevity. He's apparently going around talking about all the top players around now who he almost bought.... but didn't and that is his fault.
A team that is built and needs smaller changes every year(in theory, if the manager is doing a good job) wouldn't need to spend as much. A new manager comes in and changes the style maybe, wants some players he likes, wants to move people on, that costs money. The longer you at at a club the less spending should be in general as you go from small tweaks as opposed to rebuilding in your style.
Ignoring that while comparing spending is pointless, ignoring wage spending is pointless.
Ignoring that spending isn't everything. Most teams have good and bad years, Liverpool had a good year and almost won a title, Arsenal had a good year and came fourth. Liverpool almost won the title spending far far less(both net spend in transfers and wage spending).
Any game is winnable by anyone, it's how Chelsea sometimes lose to a crap team and how a crap team sometimes beats Chelsea. Over 10 years Arsenal by luck should have had a "good" year by now where we are actually in with a real shot of the league. A good manager can take a team and make them better, Arsenal haven't gotten better in years. We've gotten worse every year while increasing spending every single year.
Many, many other teams in europe and england have with smaller budgets than Arsenal let alone CHelsea won league, fa cups and done better in the league. Utd were being outspent by Chelsea... but won titles, Chelsea are being outspent by City significantly... but are likely to win the title. Huge wage spending and huge squads are part of but not the entire equation
Wenger has every possible advantage you can have, longevity, ability to build a team over a decade not two years, ability to buy youngsters for cheap and bring them through, ability to improve players, ability to improve tactics and simply having a lucky season. Look at Newcastle, or Everton, all teams have good and bad years. Atletico won the title against two teams that spend way more than Arsenal, while spending less than Spurs, they got to the champs league final as well despite the small squad.