There are a bunch of reasons why Tesla doesn't partner with Waymo.
The practical issue is t hat Waymo uses more advanced sensors than Tesla vehicles use. Partnering with Waymo would mean telling Tesla owners and Tesla shoppers "your vehicles won't be self-driving."
If Tesla partners with Waymo, they're telling investors that their self-driving technology won't cut it. It's not just about ego. If Tesla is worth 10x more than GM or 100x more than Mazda because of a self-driving/AI/robo-taxi future, then partnering with Waymo is essentially saying "we'll provide the easily replaceable piece of the self-driving system."
Let's say that this works by Waymo buying Tesla vehicles for its self-driving fleet. That leaves all the power in Waymo's hands. Maybe they ink an exclusive deal for a few years. When that deal is up, Waymo is going to be pitting Tesla/GM/Volkswagen/Toyota/etc. all against each other on price. Waymo has the thing they don't have. They all have mostly comparable substitutes.
Let's say it works by Tesla licensing Waymo's technology and ditching their own AI plans. Again, it leaves the power in Waymo's hands. A few years out when the deal is set to be renewed, Waymo has a dozen car companies clamoring for its technology. Waymo knows it can seek a very high price, especially if Tesla wants to keep it exclusive. If Tesla doesn't want to keep it exclusive, then Tesla's valuation needs to be a lot lower like all the other car companies.
And what's in this for Waymo? They could partner with any number of car companies. What is Tesla bringing to the table? A CEO likely to damage Waymo's reputation and blame them for anything that goes wrong?
In terms of sharing things vs. not: you're kinda getting down to a fundamental inefficiency in our whole society. If all the car companies worked together on engines, we could get better engines faster. If all the drug companies worked together, we could accelerate research. But there are problems to that idea too. Having a single way of doing data collection can lead to blind spots, having a single hierarchy can mean that different things don't get tried, etc. There's also the issue of whose work gets deemed worthy of compensation.
If you've ever worked at a large enough company, you'll have seen instances where people with entrenched ideas stymie progress. If everyone partnered on self-driving, who decides what sensors are going into the vehicles? Maybe I come up with a new sensor and SelfDrivingPartnership says "nah, we don't think it's worth the cost," and I can never test whether I'm right or not.
In some ways, open source tries to solve some of this: everyone can still compete to make something better with the freedom to do so, but you can just take other people's code so you don't have to duplicate efforts. Of course, the problem there can be that companies don't want to share the pieces that are worth a lot of money. If self-driving tech is worth a trillion dollars, I might rather get that trillion dollars for myself and you can wait another 2, 5, 10, 20 years for it to be available.