DC 20 persuasion auto success is fun. How the bonuses get there directly impacts what levels it becomes available. That 14 starting CHA means it's there at 10th level with expertise. The wood elf example that has 10 CHA gets the same option but not until 13th level. The wood elf example with 14 CHA can do the same thing at the same time.
Well, 11th, when reliable talent comes on, but sure. If auto-succeeding at difficult persuasion rolls is a high priority, then probably wood elf is not the right choice, but half-elf would do better. Start with 8,16,14,12,13,14, max DEX by 8th, maybe take Observant at 10th, and have auto 20s in two CHA-skills by 11th. You're down one each in STR and INT compared to the human, but get two more proficiencies, and if you choose can get INT to 14 by 12th so now you're auto-succeeding on DC 20 Investigation rolls too (but yes, at the cost of delaying getting CHA to 18 for those auto-20s on non-expertised skills).
I would point out going wood elf gives only penalties to the abilities scores in comparison at this point. These are minor in STR and INT but they still exist. Matching the ability score spread was impossible for the elf and ended up with minor concessions.
Yup, I've granted that all along --- they get more ability points, so on a pure stat-to-stat comparison where even spread is valued, they come out ahead. But the stats you're behind in as an elf or half-elf are by definition your two lowest priorities. If you feel the need to specialize in disparate skills (such as stealth, perception, investigation and persuasion as in your example), then yes, standard human will be able to hit all of those auto 20s a little sooner. My main point is just that the price they pay for that (1-2 skills where they have proficiency are the main ones in this hypothetical no-combat campaign) is likely to be higher than the benefit they get, in terms of how often those rolls are likely to come up. And if there is any amount of combat, they spent 9 levels (or however many it is from where you start until level 10) behind in AC, attacks, and stealth.