In the vaccination you received, there was a controlled dosage of the active ingredient. This had been tested in thousands of people and is known to give a certain amount of immune response and an acceptable amount of side effects.
When you get have contact with someone who is infectious there is a huge variation in how much viral load they might have and how much they shed. So the first person you mean might only "gift" you a tiny dose that doesn't improve your post-vaccination immunity much at all. The next day you might meet a super contagious person, get basically drenched in viral particles, and then have a breakthrough case that makes you sick for weeks.
It's the sort of "clever hack" that probably sounds appealing to a lot of software engineers but is a terrible public health plan.
That was great at the time, but today's vaccines are just a much better and more targetted way of creating immunity.
So no need to get Covid the "natural way". If you are fully vaccinated, you are fully vaccinated. As long as there is no new escape variant you are fine already.
The third shot might be pretty optional for young people, we will have to see. Still even if necessary, it is not like you have to get a shot every week, the third will probably last much longer.
Do you have a source for this? I feel like many articles/studies I've read state the opposite, i.e., vaccine immunity > natural immunity.