As a fellow lifelong driver in California, I gotta agree with some others in this thread.
The posted limit on CA freeways is only loosely-related to the actual flow of traffic. My suggestion is that if you can't use an HOV lane, stay out of the number one lane (furthest on the left, often called the 'fast' lane). You can do 74mph all day long in the middle or rightmost lanes, but when the posted limit is 70 that means prevailing speeds will easily be 80-85+. This is true even where the posted limit is 65 mph in free-flowing conditions. I know this because as a sportbike rider I don't often like to go over 80-83 (mostly due to wind and tickets) but even in the HOV lane I will get people occasionally roaring up on my six. I usually just let them pass. If I come upon someone doing 65 mph, that's considered way too slow for the HOV (in free-flowing conditions) and I will pass these people with impunity (where others just get stuck).
I love the fact that you're writing about your first trip in a Model 3, the very same car I plan to get, but yes this is easily solved if you stay out of the 'fast' lanes when you want to go 74 or slower (especially in a 70 zone where prevailing speeds are much faster). HOV lane is an exception, but even at 74 mph you will find people who are going way too slow and make the HOV less beneficial or efficient for your chosen speed.
Of course, you don't want to be one of those people who confuses posted limit with what people should be doing. Attempting to 'enforce' the speed limit (not that you were doing this) is a bad idea. The prevailing speed is the safest speed on the freeway as it reduces speed disparity and lane-changes (which are the biggest causes of accidents, especially on surface streets). This is why the CA DMV recommends one merge at flow-of-traffic speeds, not within the 'speed limit'. When speed limits are too low, there are more lane-changes (as people have their own idea of what is safe for conditions) and more lane-changes=more accidents.
This is why surface street speed limits are established by an engineering and traffic survey which measures the 85th percentile of drivers without the influence of a traffic-control device in free-flowing conditions. Speed limits are not set by the slowest drivers or by 'concerned citizens', because slower isn't safer if there's too much speed disparity causing too many lane-changes. All of these speed-based road-rage issues are more easily avoided by better lane choices.
I agree that it may not just be a Tesla issue, but it could be a little of column A and B.
Congrats on the awesome new Tesla!