Players have to live within 90 minutes (by public transport) of their youth team. The best way around this is to move a lad into the area of a club.
Accommodation and full time education is required, so to poach a players from another club needs those facilities, and they are expensive.
Brentford have three clubs almost within their part of West London and probably don't need to set up their own full academy. like Palace before, they probably have first dibs on young players at the other clubs in the area. It seems to be working.
Having an academy will stop a young player making the impassioned plea to mve to another academy with the same facilities and for any other academy to be able to claim superior facilities.
What Palace must do is ensure a young player has reason to feel he has that chance. Some clubs do it quite often and so must Palace.

The club do have (or certainly used to) a register of 'foster homes' in the cachement area for the younger players , usually older Mum's whose children have left home. The club pays them a monthly fee for bed and breakfast (all other meals at the Academy) and laundry etc., with the added bonus of them being able to provided a home-from-home experience and keep an eye on what they get up to!

As a CAT 1 Academy Palace will receive around £4.75M from the EFL / PL each year to fund the running of the Academy.

The Academy is there to develop players for the future of the game (not just for Palace) hence the funding by the EFL/PL.
Players of all ages in the Academy are aware of this as it's stated many times throughout their football journey - the goal is to develop them into professional players and if Palace release them before scholarship / professional contracts for whatever reason then the club usually try to open doors with other clubs (the academy circuit is a very close knit community).

The main cost to Palace for the Academy has been the initial build and development - without which Palace could not compete for the best (and most lucrative sell on possibility) talent as most London PL clubs facilities were much more attractive to youngsters than training at Beckenham goals...Palace facilities can now favourably compete with Fulham at MP, Chelsea at Cobham, Arsenal at Hale end and Spurs at Enfield.

To give an indication of numbers of youth players, I think a CAT 1 Academy can register around 250 players within all age groups with the PL.

Once the fixed costs are covered / paid for the only running costs will be the day to day running expenses (food and maintenance), Coach travel to away games for the U16s to U18's - Many of the Academy coaches / physios / analysts / education dept are part time and coach in the evenings whilst doing other day jobs (external or within the club) or studying degrees. Kit & training kit will be covered by the sponsors.

Only major salaries to cover will be the 'Heads of' who run each Academy section.

A couple of high value sales of Academy graduates and the initial build outlay will be recovered and Palace will be sitting on a very valuable future asset.

Not sure if any of the above also affects FFP as well.

Thanks Isley. Always nice to learn things one didn't know even at my age (I'm drawing my pension).