The irony of his position on "financial independence" so as to avoid the sort of pressure brought to bear on his mother, is that it was his mother's early death that is enabling this decision. The Princess of Wales only had a lot of money at the time of her death because her divorce had recently been finalized, had she lived, she almost surely would have spent that settlement down to nearly nothing by this point (she was well-known for being unable to manage money, even before her marriage.) The British royal family has a tradition of keeping everyone except the Sovereign & the Heir Presumptive rather cash-poor; for one thing, it helps to keep their public behavior in line. If the Duke had not inherited a huge sum of money that was held in trust and managed for him for 20 years, he would still probably be serving as active-duty Army.
FTR, the Civil List was abolished quite a while ago; now the Queen pays some expenses directly from her personal funds, while the Sovereign Grant pays out compensation for work performed (such as official goodwill tours, etc.) Grace & Favor residences are owned by the Crown and in the gift of the Sovereign, but that "gift" is actually a life estate; they cannot sell those properties. If the Sussex family gives up royal duties entirely, they could end up turfed out of Frogmore House if they don't take up the cost of upkeep, because it is part of the Sovereign's personal estate, but as it is an historic structure, upkeep is supported by the Sovereign Grant.
My understanding is that the major fly in the ointment, financially speaking, is security. The Sovereign Grant estimates security for that family costs around $6.5M(US) each year, and their personal fortunes amount only to about 4X that. Cutting security costs is likely to severely curb this bi-continental lifestyle they plan to pursue, unless the Duchess returns to her former career (which I can't see happening, because of the increased cost of insuring her on-set. Professionally, she's no Meryl Streep, so I doubt many producers would consider the cost to be worth it.) Of course, now that the mighty Weinstein Company has crumbled, there is always the chance that someone plans to step into that gap and try to produce film and TV for a living.