[RPG] the purpose of Finesse Rogue when core rules state a rogue can take any feat naturally

Your 7th level rogue has 1HP. Rogue takes 10 points of damage (which brings her to -9HP). In response, the talent activates and gives 7tHP (bringing the total to -2). You are still unconscious, but you now have 6 rounds to have a buddy pour a healing potion down your throat, attempt first aid, or for you to stabilize normally.

Assuming instead that the damage is 5 points (instead of the 10 you use in your question), the pattern goes: 1HP, -5HP from attack (to -4). Resiliency kicks in giving 7tHP (bringing total to +3). Now the Rogue has the opportunity to withdraw, and drink the healing potion in her backpack. Or perhaps beg a heal spell from the Cleric.

If your game uses the anti-hero optional rule for the hero points optional rule system you can gain a non-class, non-race, non-level-derived bonus feat. This is the only way to gain an intrinsic bonus feat without spending class or race resources on it.

If you are a half-elf or can pretend to be one Paragon Surge, by far the best spell in the game before the nerf-bat hit it, can get you another 'feat for which you meet the prerequisites' which is effectively a bonus feat. It only lasts 1 minute/level so it's not too useful to you.

You can get tons of feats from ioun stones, which would let you qualify for class entry, but you stated that you aren't interested in equipment based solutions so we wont go into detail on that.