Arsenal are there because along with United and Liverpool they are the most prestigious club from England. Just look at the other 2 main board members Real and Juve the 2 most prestigious clubs of Spain and Italy. Most domestic titles.
United and Liverpool need Arsenal and Spurs involved to stop them closing the gap financially basically keeping an eye on them and London is the bigger market. They make shyt load of money and have something that both United and Liverpool don't have modern stadiums. Yes work on Anfield has been done in the last few years. But Liverpool been trying to leave Anfield for a long time.