Yes, really.
Klopp will stay at Liverpool for as long as he wants, even if he doesnt win anything again. Why? Because he has Liverpool in the best competitions, consistently so. The reason he hasnt been sacked for finishing 5th has far less to do with the trophies he has won. Its got more to do with the fact that he has delivered 6 x top 4 finishes, in 7 years.
Yes, trophies are important and what we want as fans of a team. But, what matters more is revenue generation and you get that from being in the best competitions, all the time. For example, Man United's season would have meant nothing if you didnt qualify for the Champions League. That was the prize of your season, and the rest outside the top trophies (PL and CL) is just icing on the cake.
Also, for the top teams, winning the PL and CL is an estimated 1 in 4 chance and 1 in 8 chance year on year. To base your ability to consistently compete on those type of odds is bad financial planning. And you will quickly find yourself in financial trouble if you hire and fire based on not winning the trophies. Arsenal are not run by pocket less owners, like Chelsea or Man City.
The 400m spend is condensed into a few seasons, but its pretty much on par with every other top team in football. So the amount in such little time can be described as a red herring. Again, every single team needs to spend money to compete. Go and have a look at your club's expenditure, or City, or Chelsea in a window last season. This is par for the course.
Arsenal have financial planning which probably go beyond a financial year. I say so because of the magnitude of expenditure in football. Committing to a 100m Rice deal over 4 years, requires the highest possible income, at the highest level of football. What that means is that you are in the top 4 every season, and probably reach the knockouts of the CL every season thereafter. Not finish 1st, then finish 12th, then finish 1st.