RICH GETTING RICHER
The essential point here, seemingly, is greed.
And it would mean that clubs are getting richer over the others, and at the expense of the others.

All organisations wish to expand revenues. But then the drive of the super clubs to control revenues, or have the lion's share, would have a detriment to the game at large.
The fact that these clubs have been chosen is not a coincidence.
They have the highest revenues in the world, according to the Deloitte 2018 Money League. And they most likely will dominate the 2019 Money League, when released. All of the clubs listed as permanent members either won leagues (City/Barca), finished high in their domestic leagues (Man U), won domestic trophies (Chelsea), or reached the latter stages of European competitions (Arsenal/Liverpool), or won major European trophies (Real Madrid).
They also command much of the commercial and sponsorship revenues of clubs in the world, and thus it's understandable how they wish to gain a larger footing.
Another factor is that many of these clubs are owned by large sporting conglomerates, or operate for the benefits of their members. As a socio of Real Madrid, having a larger dividend from this competition is tempting.
To FSG of Liverpool, or KSE of Arsenal, or the Glazers of Manchester United, or the Qatar Group of Man City, why wouldn't they want to participate? I'm sure Abramovich of Chelsea would want to also, and the Qatar Group would benefit doubly via PSG's "ringfenced" position.
Will this league happen? I believe it will, though maybe not in the form that has been "leaked". Maybe UEFA and FIFA, in the interest of the global game, will seek to compromise or allow a "super" Champions League featuring these clubs. Possibly they may get these clubs to ensure the grassroots of football are protected, to try and even the playing field.
What's certain is that this has been on the agenda for a while, and given the financial rewards available, it's unlikely that this prospect will dissolve soon.