The owners have got you stuck in a catch-22. Yes, top 4 every season balances the books nicely. And yes, take it from a Spurs fan that it IS an incredible achievement that no other club can boast of. But the reality is that the same thing preventing the board from acting - finance - is the same thing that will prevent you from ever progressing. Your spending power will probably never be as robust as United, City or even Chelsea. Unless a new, mega-wealthy owner steps in who, unlike Kroenke/Gazidis treat the club as their own personal vanity project, the only other recourse to close that gap is to grow the club's global brand name and image. The fact that United's revenue continues to grow exponentially year on year despite relatively awful seasons is testament to their global reach and brand power. But the only way for Arsenal to achieve this is to chance upon an extremely marketable player (such as Bale, Ibra, Rooney) and to win major trophies. I'd wager that Leicester's global fanbase grew more in one season than Arsenal's has in a decade. Fans outside of the UK are generally glory-hunters who will follow the yellow brick road rather than actual footballing history. And the yellow-brick road is paved with trophies. Finishing 4th, not competing for the title and being dumped out of the CL relatively early on does almost nothing to boost your global revenue.
So, the board happily keeps you in the top 4 because it pays for you to remain in the top 4. It cannot pay for anything more because of the revenue gap you suffer on 2-3 much bigger clubs. It's a classic vicious cycle that someone with balls will eventually have to break and take a risk on a new man with a new plan.