Why are you putting Everton in Arsenal's shoes and switching the roles? Obviously, everyone would gloat at not giving their rivals the title, but to actively root against your team when there is something on the line is exactly why small clubs are small clubs.
If Spurs, Everton or pre oil Man City had the chance for Champions League and being consistently top 4 they should be jumping at it. Who cares if your bigger rival wins another trophy to add to their 50 others. That's my point. How you gonna catch up and not be the "smaller team" otherwise? Without cheating