During the early days when Singapore was more pro-immigrant and SPRs were handed out like hot cakes to the 1st Gens, all the young 2nd Gens (mostly PRCs) that that I came to know of which that went into local schools were almost passable as true blue Singaporean, except when they started to talk in their mother-tongue/slang with their family members - I would think there is some peer pressure or fear of being alienated that got them assimilated with the rest of their peers at school and even outside of school.
Fast forward today, I would tend to see those aspiring young 1st Gens, at least for the I and O group, that underwent at least an undergraduate programme in local public university and got their first degree locally would be at the top most priority in terms of successful SPR application. Others would be competing on whatever limited slots that are leftover - and most of them are competing purely based on residential period, financial stability, etc. with no clear commitment/potential in sinking roots.
Long gone were the days where one could game the system by doing donation and/or charity work in return for recommendation letters from MPs to boast their "grassroot" connection. The only brownie point that aspiring but older 1st Gens has would only be their children - the 2nd Gens (and preferably, the cannon fodders). But I do agree it is damn hard for foreign kids in getting P1 given the limited slots, or perhaps no slots at all when it comes to Phase 3 nowadays.
No one can guarantee whether after one is being granted SPR, will one not jump ship? It is just a simple step of SPR renunciation with CPF withdrawn and HDB flipped - the SPR label just doesn't stick to those that aren't assimilated well enough or at least accepted the ethos and norms of Singapore as most are no longer a white canvas with rooms to be painted. IMHO, the 2nd Gens are far more valuable than any 1st Gens in terms of social integration, especially after their white canvas got painted (or brainwashed) by the local education system.
Nevertheless, local education since young either for aspiring 1st Gens or 2nd Gens might not be the determining factor in a successful SPR application, but it would probably weight more than just purely harping on one's
condo, car, job, salary, etc. or how much one loves Singapore but Singapore doesn't loves back - with the S Pass and EP criteria being tightened over time, so will the SPR criteria.
sharing my story to add to the stats. 
), it is in fact possible to successfully register at a local school. Not easy, but it is possible. Of course, given the difficulties, it's easy to understand why someone would choose not to.